Unit 1 cayley-hamilton theorem lecture 1
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The document provides an overview of the Cayley-Hamilton theorem in linear algebra. It introduces the characteristic equation and lists prerequisites like matrices. It provides links to YouTube videos about finding the square and cube of a matrix and calculating the determinant. The document states that according to Cayley-Hamilton, every square matrix satisfies its own characteristic equation. It concludes by thanking the reader.
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Cayley – hamiltion theorem By Sunny
Cayley – hamiltion theorem By SunnyMd.Sunny B.Sc in Electical and Electrionic Engineering at Daffodil International University
The Cayley-Hamilton theorem states that every square matrix satisfies its own characteristic equation. Specifically, if f(λ) is the characteristic polynomial of a matrix A, then f(A) is the zero matrix. This allows any power of a matrix to be expressed in terms of lower powers. The theorem has applications in calculating functions of matrices and in fields like control systems and electrical circuits.Cayley Hamilton Theorem
The Cayley-Hamilton theorem states that every square matrix satisfies its own characteristic equation. It was independently discovered by Arthur Cayley and William Rowan Hamilton in the 1850s. Cayley proved it for 2x2 and 3x3 matrices, while Hamilton proved it for quaternion matrices. The theorem allows powers of a matrix A to be expressed as combinations of lower powers of A. This makes it useful for finding inverses and powers of matrices. It has applications in fields like robotics, encryption, and electrical circuits.
Matrices ppt
Here are the key steps to find the eigenvalues of the given matrix:
1) Write the characteristic equation: det(A - λI) = 0
2) Expand the determinant: (1-λ)(-2-λ) - 4 = 0
3) Simplify and factor: λ(λ + 1)(λ + 2) = 0
4) Find the roots: λ1 = 0, λ2 = -1, λ3 = -2
Therefore, the eigenvalues of the given matrix are -1 and -2.
Sequences and Series
This document discusses sequences and their limits. Some key points:
- A sequence is a list of numbers written in a definite order. It can be thought of as a function with domain the positive integers.
- The limit of a sequence is defined as the number L such that the terms of the sequence can be made arbitrarily close to L by choosing a sufficiently large term.
- A sequence converges if it has a finite limit, and diverges if its terms approach infinity. Bounded monotonic sequences are guaranteed to converge.
- Properties of sequence limits parallel those of limits of functions, including laws of limits and the ability to pass limits inside continuous functions.
4.3 Determinants and Cramer's Rule
This document discusses determinants and Cramer's rule. It defines determinants as special numbers associated with square matrices. It provides examples of calculating determinants of 2x2 and 3x3 matrices by rewriting columns and multiplying diagonals. The document also introduces Cramer's rule as a method to solve linear systems using determinants, where the variable is replaced with constants in the coefficient matrix. Examples are given to demonstrate solving 2x2 and 3x3 systems using Cramer's rule.
application of complex numbers
The document discusses quaternions and their applications. It begins by providing a brief history of quaternions, defined by Sir William Rowan Hamilton in 1843. Quaternions represent rotations and orientations in 3D space and are used in computer graphics, control theory, physics, and other fields due to advantages like avoiding gimbal lock. The document then covers details of quaternion operations like addition, multiplication, and rotation representations. It provides examples of using quaternions to represent and perform rotations in three dimensions.
Word Problems
The document provides an overview of solving word problems, explaining the process as reading the problem, representing unknowns with variables, relating the unknowns to given values, writing an equation, solving the equation, and proving the answer. It also defines odd, even, and consecutive numbers and provides examples of representing and solving word problems involving these types of numbers.
Determinants
This document provides information about determinants of square matrices:
- It defines the determinant of a matrix as a scalar value associated with the matrix. Determinants are computed using minors and cofactors.
- Properties of determinants are described, such as how determinants change with row/column operations or identical rows/columns.
- Examples are provided to demonstrate computing determinants by expanding along rows or columns and using cofactors and minors.
- Applications of determinants include finding the area of triangles and solving systems of linear equations.
Recommended
Cayley – hamiltion theorem By Sunny
Cayley – hamiltion theorem By SunnyMd.Sunny B.Sc in Electical and Electrionic Engineering at Daffodil International University
The Cayley-Hamilton theorem states that every square matrix satisfies its own characteristic equation. Specifically, if f(λ) is the characteristic polynomial of a matrix A, then f(A) is the zero matrix. This allows any power of a matrix to be expressed in terms of lower powers. The theorem has applications in calculating functions of matrices and in fields like control systems and electrical circuits.Cayley Hamilton Theorem
The Cayley-Hamilton theorem states that every square matrix satisfies its own characteristic equation. It was independently discovered by Arthur Cayley and William Rowan Hamilton in the 1850s. Cayley proved it for 2x2 and 3x3 matrices, while Hamilton proved it for quaternion matrices. The theorem allows powers of a matrix A to be expressed as combinations of lower powers of A. This makes it useful for finding inverses and powers of matrices. It has applications in fields like robotics, encryption, and electrical circuits.
Matrices ppt
Here are the key steps to find the eigenvalues of the given matrix:
1) Write the characteristic equation: det(A - λI) = 0
2) Expand the determinant: (1-λ)(-2-λ) - 4 = 0
3) Simplify and factor: λ(λ + 1)(λ + 2) = 0
4) Find the roots: λ1 = 0, λ2 = -1, λ3 = -2
Therefore, the eigenvalues of the given matrix are -1 and -2.
Sequences and Series
This document discusses sequences and their limits. Some key points:
- A sequence is a list of numbers written in a definite order. It can be thought of as a function with domain the positive integers.
- The limit of a sequence is defined as the number L such that the terms of the sequence can be made arbitrarily close to L by choosing a sufficiently large term.
- A sequence converges if it has a finite limit, and diverges if its terms approach infinity. Bounded monotonic sequences are guaranteed to converge.
- Properties of sequence limits parallel those of limits of functions, including laws of limits and the ability to pass limits inside continuous functions.
4.3 Determinants and Cramer's Rule
This document discusses determinants and Cramer's rule. It defines determinants as special numbers associated with square matrices. It provides examples of calculating determinants of 2x2 and 3x3 matrices by rewriting columns and multiplying diagonals. The document also introduces Cramer's rule as a method to solve linear systems using determinants, where the variable is replaced with constants in the coefficient matrix. Examples are given to demonstrate solving 2x2 and 3x3 systems using Cramer's rule.
application of complex numbers
The document discusses quaternions and their applications. It begins by providing a brief history of quaternions, defined by Sir William Rowan Hamilton in 1843. Quaternions represent rotations and orientations in 3D space and are used in computer graphics, control theory, physics, and other fields due to advantages like avoiding gimbal lock. The document then covers details of quaternion operations like addition, multiplication, and rotation representations. It provides examples of using quaternions to represent and perform rotations in three dimensions.
Word Problems
The document provides an overview of solving word problems, explaining the process as reading the problem, representing unknowns with variables, relating the unknowns to given values, writing an equation, solving the equation, and proving the answer. It also defines odd, even, and consecutive numbers and provides examples of representing and solving word problems involving these types of numbers.
Determinants
This document provides information about determinants of square matrices:
- It defines the determinant of a matrix as a scalar value associated with the matrix. Determinants are computed using minors and cofactors.
- Properties of determinants are described, such as how determinants change with row/column operations or identical rows/columns.
- Examples are provided to demonstrate computing determinants by expanding along rows or columns and using cofactors and minors.
- Applications of determinants include finding the area of triangles and solving systems of linear equations.
Real Numbers
The document defines several subsets of real numbers including natural numbers, whole numbers, integers, rational numbers, and irrational numbers. It provides examples for each set and discusses their properties. Rational numbers can be expressed as terminating or repeating decimals while irrational numbers are expressed as non-terminating, non-repeating decimals. The document also covers topics like the Euclid division algorithm, fundamental theorem of arithmetic, finding the highest common factor and least common multiple of numbers.
Limits And Derivative
The document discusses key concepts in calculus including functions, limits, derivatives, and derivatives of trigonometric functions. It provides examples of calculating derivatives from first principles using the definition of the derivative and common derivative rules like the product rule and quotient rule. Formulas are also derived for the derivatives of the sine, cosine, and tangent functions.
Taylor and Maclaurin Series
Taylor and Maclaurin Series are representations of functions as infinite sums of terms calculated from the function's derivatives at a single point. Specifically, a Taylor series expands a function around some point a, while a Maclaurin series is the special case of a Taylor series expanded around zero. Examples are provided of using Taylor series to expand the square root function around 1 and finding the Maclaurin series for the sine function.
Applications of system of linear equations.ppt
Word problems involving systems of linear equations in two variables. Solving simultaneous equation problems by elimination and substitution. Application of simultaneous equations.
Disclaimer: Some parts of the presentation are obtained from various sources. Credit to the rightful owners.
9.3 Solving Systems With Gaussian Elimination
Write the augmented matrix of a system of equations.
Write the system of equations from an augmented matrix.
Perform row operations on a matrix.
Solve a system of linear equations using matrices.
An introdcution to complex numbers jcw
The document introduces complex numbers and different ways to represent them, including:
1) Imaginary numbers, represented by i, which allows for solutions to equations with "hidden roots". Complex numbers have both a real and imaginary part.
2) Polar form represents complex numbers using modulus (distance from origin) and argument (angle from positive x-axis).
3) Exponential or Euler's form uses modulus and an imaginary exponent to represent complex numbers, where the angle must be in radians.
4) Operations like addition, subtraction, multiplication and division are introduced for complex numbers, along with converting between rectangular, polar and exponential forms.
Composite functions
This document discusses composite functions. It defines a composite function as when a number or letter is affected by more than one function. It provides examples of combining different functions, such as f(x) = 3x and g(x) = x^2, and explains that the order matters as f(g(x)) is not the same as g(f(x)). The document then shows how to write composite functions using formulas, such as if f(x)= 2x + 1 and g(x) = 4x, then f(g(x)) = 2(4x) + 1 = 8x + 1 and g(f(x)) = 4(2x + 1) = 8x
Introduction to algebra
Algebra uses letters and symbols to represent values and their relationships, especially for solving equations. An algebraic expression combines these letters and symbols. An example expression is 8x^2. Expressions contain constants, variables, and exponents. Constants represent exact values like numbers. Variables stand for unknown values, often letters. Exponents written above a variable show how many times it is used in the expression.
Determinants
The document defines determinants as values that can be computed from the elements of a square matrix. Determinants are used throughout mathematics, including in solving systems of linear equations, change of variables rules for integrals, eigenvalue problems, and expressing volumes of parallelepipeds. The determinant of a matrix product equals the product of the determinants, showing that the determinant is a multiplicative map. A matrix is invertible if and only if its determinant is non-zero.
Matrices And Determinants
Matrices are widely used in business, economics, and other fields. They allow problems to be represented with distinct finite numbers rather than infinite gradations as in calculus. Sociologists, demographers, and economists use matrices to study groups, populations, industries, and social accounting. [/SUMMARY]
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This document presents an overview of the Laplace transform and its applications. It begins with an introduction to Laplace transforms as a mathematical tool to convert differential equations into algebraic expressions. It then provides definitions and properties of both the Laplace transform and its inverse. Examples are given of how Laplace transforms can be used to solve ordinary and partial differential equations, as well as applications in electrical circuits and other fields. The document concludes by noting some limitations of the Laplace transform method and references additional resources.
Properties of whole numbers in addition and multiplication
This document discusses properties of whole numbers in addition and multiplication. It covers the closure or uniqueness property, commutative property, associative property, identity properties in addition and multiplication, zero property in multiplication, and distributive property of multiplication. For example, the closure property states that the sum or product of two whole numbers is also a whole number. The commutative property means the order of numbers does not change the sum or product.
Application of Linear Algebra in Electrical Circuit
Perhaps one of the most apparent uses of linear algebra is that which is used in
Electrical Engineering. As most students of mathematics have encountered, when the
subject of systems of equations is introduced, math class is temporarily converted into a
crash course in electrical components. There, the resistor, voltage source and capacitor
take the stage as well as their accompanying language consisting of Kirchoff and Ohm.
With the basic concepts down, math class is resumed and students can look forward to
playing with n number of equations with n number of unknowns. To solve for the
currents and voltages, students can use simplification and substitutions, but with many
equations, this task quickly becomes very time consuming and tedious.
However, using Gaussian Elimination along with computers, engineers are able to
efficiently calculate unknown values of extremely large and complex systems without
performing hundreds of calculations and exhaustive bookkeeping of values
Square Roots And Perfect Squares
The document introduces square roots by explaining that the square root of 25 is 5 because 5 x 5 equals 25, and the square root of 49 is 7 because 7 x 7 equals 49. These numbers that have whole number square roots are called perfect squares. The document also includes a table showing the first 15 perfect squares and their corresponding square roots that should be memorized.
Binomial Distribution Part 5
Binomial Distribution Part 5 deals with fitting & familiaring some concepts of B D under the complementary Statistics syllabus of University of Calicut in BSc core of Mathematics, Physics & Computer Science.
Algebra basic introduction
Algebra was developed as a separate section of mathematics to solve problems involving unknown numbers. In algebra, unknown numbers are represented by variables like x, allowing problems to be solved using the same addition, subtraction, etc. operations as regular arithmetic. For example, if the number of boys in a class is unknown and represented by x, we can write an equation relating x to the total number of students and known number of girls to solve for x. Algebra introduces variables like x to represent unknowns, but applies the same basic math operations as used with numbers.
Use of matrix in daily life
What is matrix? Matrix in physics. Matrix in computer science. Matrix in encryption. Matrix in others sector. geology surveys,robot movement,scientific experiment.
Determinants
The document discusses determinants and their properties. It defines determinants as representing single numbers obtained by multiplying and adding matrix elements in a special way. It then provides formulas for calculating determinants of matrices of order 1, 2 and 3. It also outlines several properties of determinants, such as how interchanging rows/columns, multiplying rows by constants, and adding rows affects the determinant. Finally, it discusses how determinants are used to determine whether systems of linear equations are consistent or inconsistent.
types of numbers
This document defines and explains different types of numbers:
1. Natural numbers are the positive whole numbers {1, 2, 3...}. Whole numbers include 0. Integers include positive and negative whole numbers. Rational numbers can be written as fractions. Irrational numbers cannot be written as fractions.
2. Real numbers include rational and irrational numbers and can be written as decimals. Complex numbers are numbers in the form a + bi, where a and b are real numbers. Complex numbers contain both real and imaginary parts.
3. The set of complex numbers contains all real and imaginary numbers. Operations on complex numbers follow specific rules: addition/subtraction combine real and imaginary parts separately, multiplication distributes and
Integration
This document discusses integration in mathematics. It defines integration as the process opposite to differentiation, where integration finds the direct relationship between two variables given their rate of change. Several techniques for integration are described, including integration by parts and substitution. The document outlines the history of integration and its applications in fields like engineering, business, and its use in estimating important values.
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Limits And Derivative
The document discusses key concepts in calculus including functions, limits, derivatives, and derivatives of trigonometric functions. It provides examples of calculating derivatives from first principles using the definition of the derivative and common derivative rules like the product rule and quotient rule. Formulas are also derived for the derivatives of the sine, cosine, and tangent functions.
Taylor and Maclaurin Series
Taylor and Maclaurin Series are representations of functions as infinite sums of terms calculated from the function's derivatives at a single point. Specifically, a Taylor series expands a function around some point a, while a Maclaurin series is the special case of a Taylor series expanded around zero. Examples are provided of using Taylor series to expand the square root function around 1 and finding the Maclaurin series for the sine function.
Applications of system of linear equations.ppt
Word problems involving systems of linear equations in two variables. Solving simultaneous equation problems by elimination and substitution. Application of simultaneous equations.
Disclaimer: Some parts of the presentation are obtained from various sources. Credit to the rightful owners.
9.3 Solving Systems With Gaussian Elimination
Write the augmented matrix of a system of equations.
Write the system of equations from an augmented matrix.
Perform row operations on a matrix.
Solve a system of linear equations using matrices.
An introdcution to complex numbers jcw
The document introduces complex numbers and different ways to represent them, including:
1) Imaginary numbers, represented by i, which allows for solutions to equations with "hidden roots". Complex numbers have both a real and imaginary part.
2) Polar form represents complex numbers using modulus (distance from origin) and argument (angle from positive x-axis).
3) Exponential or Euler's form uses modulus and an imaginary exponent to represent complex numbers, where the angle must be in radians.
4) Operations like addition, subtraction, multiplication and division are introduced for complex numbers, along with converting between rectangular, polar and exponential forms.
Composite functions
This document discusses composite functions. It defines a composite function as when a number or letter is affected by more than one function. It provides examples of combining different functions, such as f(x) = 3x and g(x) = x^2, and explains that the order matters as f(g(x)) is not the same as g(f(x)). The document then shows how to write composite functions using formulas, such as if f(x)= 2x + 1 and g(x) = 4x, then f(g(x)) = 2(4x) + 1 = 8x + 1 and g(f(x)) = 4(2x + 1) = 8x
Introduction to algebra
Algebra uses letters and symbols to represent values and their relationships, especially for solving equations. An algebraic expression combines these letters and symbols. An example expression is 8x^2. Expressions contain constants, variables, and exponents. Constants represent exact values like numbers. Variables stand for unknown values, often letters. Exponents written above a variable show how many times it is used in the expression.
Determinants
The document defines determinants as values that can be computed from the elements of a square matrix. Determinants are used throughout mathematics, including in solving systems of linear equations, change of variables rules for integrals, eigenvalue problems, and expressing volumes of parallelepipeds. The determinant of a matrix product equals the product of the determinants, showing that the determinant is a multiplicative map. A matrix is invertible if and only if its determinant is non-zero.
Matrices And Determinants
Matrices are widely used in business, economics, and other fields. They allow problems to be represented with distinct finite numbers rather than infinite gradations as in calculus. Sociologists, demographers, and economists use matrices to study groups, populations, industries, and social accounting. [/SUMMARY]
Laplace Transformation & Its Application
This document presents an overview of the Laplace transform and its applications. It begins with an introduction to Laplace transforms as a mathematical tool to convert differential equations into algebraic expressions. It then provides definitions and properties of both the Laplace transform and its inverse. Examples are given of how Laplace transforms can be used to solve ordinary and partial differential equations, as well as applications in electrical circuits and other fields. The document concludes by noting some limitations of the Laplace transform method and references additional resources.
Properties of whole numbers in addition and multiplication
This document discusses properties of whole numbers in addition and multiplication. It covers the closure or uniqueness property, commutative property, associative property, identity properties in addition and multiplication, zero property in multiplication, and distributive property of multiplication. For example, the closure property states that the sum or product of two whole numbers is also a whole number. The commutative property means the order of numbers does not change the sum or product.
Application of Linear Algebra in Electrical Circuit
Perhaps one of the most apparent uses of linear algebra is that which is used in
Electrical Engineering. As most students of mathematics have encountered, when the
subject of systems of equations is introduced, math class is temporarily converted into a
crash course in electrical components. There, the resistor, voltage source and capacitor
take the stage as well as their accompanying language consisting of Kirchoff and Ohm.
With the basic concepts down, math class is resumed and students can look forward to
playing with n number of equations with n number of unknowns. To solve for the
currents and voltages, students can use simplification and substitutions, but with many
equations, this task quickly becomes very time consuming and tedious.
However, using Gaussian Elimination along with computers, engineers are able to
efficiently calculate unknown values of extremely large and complex systems without
performing hundreds of calculations and exhaustive bookkeeping of values
Square Roots And Perfect Squares
The document introduces square roots by explaining that the square root of 25 is 5 because 5 x 5 equals 25, and the square root of 49 is 7 because 7 x 7 equals 49. These numbers that have whole number square roots are called perfect squares. The document also includes a table showing the first 15 perfect squares and their corresponding square roots that should be memorized.
Binomial Distribution Part 5
Binomial Distribution Part 5 deals with fitting & familiaring some concepts of B D under the complementary Statistics syllabus of University of Calicut in BSc core of Mathematics, Physics & Computer Science.
Algebra basic introduction
Algebra was developed as a separate section of mathematics to solve problems involving unknown numbers. In algebra, unknown numbers are represented by variables like x, allowing problems to be solved using the same addition, subtraction, etc. operations as regular arithmetic. For example, if the number of boys in a class is unknown and represented by x, we can write an equation relating x to the total number of students and known number of girls to solve for x. Algebra introduces variables like x to represent unknowns, but applies the same basic math operations as used with numbers.
Use of matrix in daily life
What is matrix? Matrix in physics. Matrix in computer science. Matrix in encryption. Matrix in others sector. geology surveys,robot movement,scientific experiment.
Determinants
The document discusses determinants and their properties. It defines determinants as representing single numbers obtained by multiplying and adding matrix elements in a special way. It then provides formulas for calculating determinants of matrices of order 1, 2 and 3. It also outlines several properties of determinants, such as how interchanging rows/columns, multiplying rows by constants, and adding rows affects the determinant. Finally, it discusses how determinants are used to determine whether systems of linear equations are consistent or inconsistent.
types of numbers
This document defines and explains different types of numbers:
1. Natural numbers are the positive whole numbers {1, 2, 3...}. Whole numbers include 0. Integers include positive and negative whole numbers. Rational numbers can be written as fractions. Irrational numbers cannot be written as fractions.
2. Real numbers include rational and irrational numbers and can be written as decimals. Complex numbers are numbers in the form a + bi, where a and b are real numbers. Complex numbers contain both real and imaginary parts.
3. The set of complex numbers contains all real and imaginary numbers. Operations on complex numbers follow specific rules: addition/subtraction combine real and imaginary parts separately, multiplication distributes and
Integration
This document discusses integration in mathematics. It defines integration as the process opposite to differentiation, where integration finds the direct relationship between two variables given their rate of change. Several techniques for integration are described, including integration by parts and substitution. The document outlines the history of integration and its applications in fields like engineering, business, and its use in estimating important values.
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Historically, mechanical engineering has relied heavily on human expertise and empirical methods to solve complex problems. With the introduction of computer-aided design (CAD) and finite element analysis (FEA), the field took its first steps towards digitization. These tools allowed engineers to simulate and analyze mechanical systems with greater accuracy and efficiency. However, the sheer volume of data generated by modern engineering systems and the increasing complexity of these systems have necessitated more advanced analytical tools, paving the way for AI.
AI offers the capability to process vast amounts of data, identify patterns, and make predictions with a level of speed and accuracy unattainable by traditional methods. This has profound implications for mechanical engineering, enabling more efficient design processes, predictive maintenance strategies, and optimized manufacturing operations. AI-driven tools can learn from historical data, adapt to new information, and continuously improve their performance, making them invaluable in tackling the multifaceted challenges of modern mechanical engineering.
Optimizing Gradle Builds - Gradle DPE Tour Berlin 2024
Sinan from the Delivery Hero mobile infrastructure engineering team shares a deep dive into performance acceleration with Gradle build cache optimizations. Sinan shares their journey into solving complex build-cache problems that affect Gradle builds. By understanding the challenges and solutions found in our journey, we aim to demonstrate the possibilities for faster builds. The case study reveals how overlapping outputs and cache misconfigurations led to significant increases in build times, especially as the project scaled up with numerous modules using Paparazzi tests. The journey from diagnosing to defeating cache issues offers invaluable lessons on maintaining cache integrity without sacrificing functionality.
Supermarket Management System Project Report.pdf
Supermarket management is a stand-alone J2EE using Eclipse Juno program.
This project contains all the necessary required information about maintaining
the supermarket billing system.
The core idea of this project to minimize the paper work and centralize the
data. Here all the communication is taken in secure manner. That is, in this
application the information will be stored in client itself. For further security the
data base is stored in the back-end oracle and so no intruders can access it.
Accident detection system project report.pdf
The Rapid growth of technology and infrastructure has made our lives easier. The
advent of technology has also increased the traffic hazards and the road accidents take place
frequently which causes huge loss of life and property because of the poor emergency facilities.
Many lives could have been saved if emergency service could get accident information and
reach in time. Our project will provide an optimum solution to this draw back. A piezo electric
sensor can be used as a crash or rollover detector of the vehicle during and after a crash. With
signals from a piezo electric sensor, a severe accident can be recognized. According to this
project when a vehicle meets with an accident immediately piezo electric sensor will detect the
signal or if a car rolls over. Then with the help of GSM module and GPS module, the location
will be sent to the emergency contact. Then after conforming the location necessary action will
be taken. If the person meets with a small accident or if there is no serious threat to anyone’s
life, then the alert message can be terminated by the driver by a switch provided in order to
avoid wasting the valuable time of the medical rescue team.
LLM Fine Tuning with QLoRA Cassandra Lunch 4, presented by Anant
Slides for the 4th Presentation on LLM Fine-Tuning with QLoRA Presented by Anant, featuring DataStax Astra
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Pressure Relief valve used in flow line to release the over pressure at our d...
Pressure Relief valve used in flow line to release the over pressure at our desired pressure
Call For Paper -3rd International Conference on Artificial Intelligence Advan...
* Registration is currently open *
Call for Research Papers!!!
Free – Extended Paper will be published as free of cost.
3rd International Conference on Artificial Intelligence Advances (AIAD 2024)
July 13 ~ 14, 2024, Virtual Conference
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Submission Deadline: June 22, 2024
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https://aiad2024.org/submission/index.php
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Unit 1 cayley-hamilton theorem lecture 1
- 1. Unit-1 Cayley-Hamilton Theorem Presented by Sivanesan G, Assistant professor, Department of Mathematics, Government college of Engineering Salem-11
- 3. Prerequisite: Matrix To Find square and cube of a Matrix Youtube channel: livemathematica Link:https://youtu.be/R2mrTvLFJ4s To find determinant value of the matrix Youtube channel: The calculator King Link:https://youtu.be/KLFwbl9VZSM
- 4. Practice problem Check the Answer
- 5. Cayley -Hamilton Theorem Every Square Matrix Satisfies its own Characteristic Equation
- 7. Problem
- 12. Thank you