A very quick and easy to understand introduction to Gram-Schmidt Orthogonalization (Orthonormalization) and how to obtain QR decomposition of a matrix using it.
Integration is a part of Calculus.
This is just a short presentation on Integration.
It may help you out to complete your academic presentation.
Thank You
The module-algebra structures of quantum enveloping algebra Uq(sl(m+1)) on the coordinate algebra of quantum vector spaces (in other words, quantum actions/symmetries) are
investigated. We denote the coordinate algebra of quantum n-dimensional vector space by Aq(n). As our main result, first, we give a complete classification of module-algebra structures of Uq(sl(m+1)) on Aq(3), and with the same method, on Aq(2), all module-algebra structures of Uq(sl(m+1)) are characterized. The classical limit of the Uq(sl(3))-module algebra
structures on Aq(2) are presented, and, as opposite to Uq(sl(2)) case, there no cubic and fourth-power terms. Lastly, the module-algebra structures of Uq(sl(m+1)) on Aq(n) are obtained for any n ≥ 4, and are classified using the language of Dynkin diagrams.
Math for Intelligent Systems - 01 Linear Algebra 01 Vector SpacesAndres Mendez-Vazquez
These are the initial notes for a class I am preparing for this summer in the Mathematics of Intelligent Systems. we will start with the vectors spaces, their basis and dimensions. The, we will look at one the basic applications the linear regression.
A very quick and easy to understand introduction to Gram-Schmidt Orthogonalization (Orthonormalization) and how to obtain QR decomposition of a matrix using it.
Integration is a part of Calculus.
This is just a short presentation on Integration.
It may help you out to complete your academic presentation.
Thank You
The module-algebra structures of quantum enveloping algebra Uq(sl(m+1)) on the coordinate algebra of quantum vector spaces (in other words, quantum actions/symmetries) are
investigated. We denote the coordinate algebra of quantum n-dimensional vector space by Aq(n). As our main result, first, we give a complete classification of module-algebra structures of Uq(sl(m+1)) on Aq(3), and with the same method, on Aq(2), all module-algebra structures of Uq(sl(m+1)) are characterized. The classical limit of the Uq(sl(3))-module algebra
structures on Aq(2) are presented, and, as opposite to Uq(sl(2)) case, there no cubic and fourth-power terms. Lastly, the module-algebra structures of Uq(sl(m+1)) on Aq(n) are obtained for any n ≥ 4, and are classified using the language of Dynkin diagrams.
Math for Intelligent Systems - 01 Linear Algebra 01 Vector SpacesAndres Mendez-Vazquez
These are the initial notes for a class I am preparing for this summer in the Mathematics of Intelligent Systems. we will start with the vectors spaces, their basis and dimensions. The, we will look at one the basic applications the linear regression.
Vector Space & Sub Space Presentation
Presented By: Sufian Mehmood Soomro
Department: (BS) Computer Science
Course Title: Linear Algebra
Shah Abdul Latif University Ghotki Campus
On the Seidel’s Method, a Stronger Contraction Fixed Point Iterative Method o...BRNSS Publication Hub
In the solution of a system of linear equations, there exist many methods most of which are not fixed point iterative methods. However, this method of Sidel’s iteration ensures that the given system of the equation must be contractive after satisfying diagonal dominance. The theory behind this was discussed in sections one and two and the end; the application was extensively discussed in the last section.
Chapter 12
Section 12.1: Three-Dimensional Coordinate Systems
We locate a point on a number line as one coordinate, in the plane as an ordered pair, and in
space as an ordered triple. So we call number line as one dimensional, plane as two
dimensional, and space as three dimensional co – ordinate system.
In three dimensional, there is origin (0, 0, 0) and there are three axes – x -, y - , and z – axis. X –
and y – axes are horizontal and z – axis is vertical. These three axes divide the space into eight
equal parts, called the octants. In addition, these three axes divide the space into three
coordinate planes.
– The xy-plane contains the x- and y-axes. The equation is z = 0.
– The yz-plane contains the y- and z-axes. The equation is x = 0.
– The xz-plane contains the x- and z-axes. The equation is y = 0.
If P is any point in space, let:
– a be the (directed) distance from the yz-plane to P.
– b be the distance from the xz-plane to P.
– c be the distance from the xy-plane to P.
Then the point P by the ordered triple of real numbers (a, b, c), where a, b, and c are the
coordinates of P.
– a is the x-coordinate.
– b is the y-coordinate.
– c is the z-coordinate.
– Thus, to locate a point (a, b, c) in space, start from the origin (0, 0, 0) and move a
units along the x-axis. Then, move b units parallel to the y-axis. Finally, move c
units parallel to the z-axis.
The three dimensional Cartesian co – ordinate system follows the right hand rule.
Examples:
Plot the points (2,3,4), (2, -3, 4), (-2, -3, 4), (2, -3, -4), and (-2, -3, -4).
The Cartesian product x x = {(x, y, z) | x, y, z in } is the set of all ordered triples of
real numbers and is denoted by 3 .
Note:
1. In 2 – dimension, an equation in x and y represents a curve in the plane 2 . In 3 –
dimension, an equation in x, y, and z represents a surface in space 3 .
2. When we see an equation, we must understand from the context that it is a curve in the
plane or a surface in space. For example, y = 5 is a line in 2 �but it is a plane in 3 �
������
3. in space, if k, l, & m are constants, then
– x = k represents a plane parallel to the yz-plane ( a vertical plane).
– y = k is a plane parallel to the xz-plane ( a vertical plane).
– z = k is a plane parallel to the xy-plane ( a horizontal plane).
– x = k & y = l is a line.
– x = k & z = m is a line.
– y = l & z = m is a line.
– x = k, y = l and z = m is a point.
Examples: Describe and sketch y = x in 3
Example:
Solve:
Which of the points P(6, 2, 3), Q(-5, -1, 4), and R(0, 3, 8) is closest to the xz – plane? Which point
lies in the yz – plane?
Distance between two points in space:
We simply extend the formula from 2 to . 3 . The distance |p1 p2 | between the points
P1(x1,y1, z1) and P2(x2, y2, z2) is: 2 2 21 2 2 1 ...
First part of description of Matrix Calculus at Undergraduate in Science (Math, Physics, Engineering) level.
Please send comments and suggestions to solo.hermelin@gmail.com.
For more presentations please visit my website at
http://www.solohermelin.com.
To give the complete list of Uq(sl2)-actions of the quantum plane, we first obtain the structure of quantum plane automorphisms. Then we introduce some special symbolic matrices to classify the series of actions using the weights. There are uncountably many isomorphism classes of the symmetries. We give the classical limit of the above actions.
This the presentation prepared by SIDI DILER the student of CIVIL ENGINEERING at Government Engineering College BHUJ under the fulfillment of the Progressive Assessment component of the Course of Vector Calculus and Linear Algebra with code 2110015.
This presentation gives the basic idea about the methods of solving ODEs
The methods like variation of parameters, undetermined coefficient method, 1/f(D) method, Particular integral and complimentary functions of an ODE
This presentation includes basic of PCOS their pathology and treatment and also Ayurveda correlation of PCOS and Ayurvedic line of treatment mentioned in classics.
A Strategic Approach: GenAI in EducationPeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
Executive Directors Chat Leveraging AI for Diversity, Equity, and InclusionTechSoup
Let’s explore the intersection of technology and equity in the final session of our DEI series. Discover how AI tools, like ChatGPT, can be used to support and enhance your nonprofit's DEI initiatives. Participants will gain insights into practical AI applications and get tips for leveraging technology to advance their DEI goals.
How to Build a Module in Odoo 17 Using the Scaffold MethodCeline George
Odoo provides an option for creating a module by using a single line command. By using this command the user can make a whole structure of a module. It is very easy for a beginner to make a module. There is no need to make each file manually. This slide will show how to create a module using the scaffold method.
MATATAG CURRICULUM: ASSESSING THE READINESS OF ELEM. PUBLIC SCHOOL TEACHERS I...NelTorrente
In this research, it concludes that while the readiness of teachers in Caloocan City to implement the MATATAG Curriculum is generally positive, targeted efforts in professional development, resource distribution, support networks, and comprehensive preparation can address the existing gaps and ensure successful curriculum implementation.
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
Introduction to AI for Nonprofits with Tapp NetworkTechSoup
Dive into the world of AI! Experts Jon Hill and Tareq Monaur will guide you through AI's role in enhancing nonprofit websites and basic marketing strategies, making it easy to understand and apply.
it describes the bony anatomy including the femoral head , acetabulum, labrum . also discusses the capsule , ligaments . muscle that act on the hip joint and the range of motion are outlined. factors affecting hip joint stability and weight transmission through the joint are summarized.
Delivering Micro-Credentials in Technical and Vocational Education and TrainingAG2 Design
Explore how micro-credentials are transforming Technical and Vocational Education and Training (TVET) with this comprehensive slide deck. Discover what micro-credentials are, their importance in TVET, the advantages they offer, and the insights from industry experts. Additionally, learn about the top software applications available for creating and managing micro-credentials. This presentation also includes valuable resources and a discussion on the future of these specialised certifications.
For more detailed information on delivering micro-credentials in TVET, visit this https://tvettrainer.com/delivering-micro-credentials-in-tvet/
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
5. • A vector space is a nonempty set V
of objects, called vectors on which
are defined two operations, called
vector addition and scalar
multiplication.
DIDNT
UNDERSTAN
D ,LETS TRY
THIS .
7. AXIOM 1
For every pair of element u and v in V
there corresponds a unique element in
V called the sum of u and v denoted by
Here V is set
and
U and v are
element
18. (1) AXIOM 1 (CLOSURE UNDER
ADDITION)
(2) AXIOM 2 (CLOSURE UNDER
MULTIPLICATION)
(3) AXIOM 5 (EXISTUNCE OF ZERO
ELEMENT)
(4) AXIOM 6 (EXISTENCE OF NEGATIVE )
19. • A subspace is a vector
space inside a vector space.
When we look at various
vector spaces, it is often
useful to examine their
subspaces.
FOR MORE
CLICK HERE
20. • The subspace S of a vector space V is that S is a subset of V
and that it has the following key characteristics
• S is closed under scalar multiplication: if λ∈R, v∈S, λv∈S
• S is closed under addition: if u, v ∈ S, u+v∈S.
• S contains 0, the zero vector.
• Any subset with these characteristics is a subspace.
PROPERTIES
21.
22. Let V = 𝑅 𝑛 be the set
X = (𝑎1 + 𝑎2 +………….+ 𝑎 𝑛) ∈ 𝑅 𝑛
Y = (𝑏1 + 𝑏2 +………….+ 𝑏 𝑛) ∈ 𝑅 𝑛
we have to show that 𝑅 𝑛
is an vector space.
23. (1) Closure : -
Since X , Y ∈ 𝑅 𝑛
𝑎1, 𝑏2 ∈ R and hence
(𝑎1 + 𝑏2) ∈ R
Therefore X + Y ∈ R
25. (3)Existence of zero element
Here the zero vector 0 = (0,0,0,……,0)
Then for any X ∈ 𝑅 𝑛
X+O = (𝑎1 + 𝑎2 +………….+ 𝑎 𝑛) + (0,0,0,………,0)
= (𝑎1 + 0, 𝑎2 + 0, 𝑎3 + 0,…………. 𝑎 𝑛 + 0)
= (𝑎1 + 𝑎2 +………….+ 𝑎 𝑛) = X
26. (4)Existence of negative
Let X ∈ 𝑅 𝑛
then
(-1)X = -X is the additive inverse of X
Since –X = (-𝑎1,- 𝑎2,…………., -𝑎 𝑛)
X + (-1) = (𝑎1, 𝑎2,…………., 𝑎 𝑛) + (-𝑎1,- 𝑎2,…………., -𝑎 𝑛)
= (𝑎1 − 𝑎1, 𝑎2 − 𝑎2, 𝑎3 − 𝑎3,………….., 𝑎 𝑛 − 𝑎 𝑛)
= (0,0,0,………,0) = 0 –X + X
28. (6)Distributive law of number
Let k ,m ∈ R, Then
(k + m)X = ((k + m) 𝑎1, (k + m) 𝑎2,…………, (k + m) 𝑎 𝑛)
= ( k𝑎1 + m𝑎1, k𝑎2 + m𝑎2,………., k𝑎 𝑛 + m𝑎 𝑛,)
=( k 𝑎1, k 𝑎2,…., k 𝑎 𝑛) + ( m 𝑎1, m 𝑎2,…., m 𝑎 𝑛)
= kX + mX
29. (7)Distributive Law for vector
addition
K ( X + Y ) = k((𝑎1 + 𝑎2 +……….+ 𝑎 𝑛) + (𝑏1 + 𝑏2 +………….+ 𝑏 𝑛))
=k(𝑎1 + 𝑏1, 𝑎2 + 𝑏2, 𝑎3 + 𝑏3,………….., 𝑎 𝑛 + 𝑏 𝑛)
= (k𝑎1 + k𝑎2 +…….+k 𝑎 𝑛) + (k𝑏1 + k𝑏2 +……+ 𝑘𝑏 𝑛)
= kX + kY
Remember k is
scalar quantity
where X and Y
are vector
quantity
31. (9)Associative law for
multiplication of numbers
For ever x in 𝑅 𝑛 and all real numbers k and m ∈ 𝑅
(km)X = (km) (𝑎1, 𝑎2,…………., 𝑎 𝑛)
= (𝑘𝑚𝑎1, km𝑎2,…………., km𝑎 𝑛)
=k (𝑚𝑎1, m𝑎2,…………., m𝑎 𝑛)
=k(m (𝑎1, 𝑎2,…………., 𝑎 𝑛) )
=k(mX)
32. • Let U be the set of all vectors of form
2r-s
3r
r+s
r,s ∈ R
Note that 2r-s
3r
r+s
=
2
3
1
r +
-1
0
1
∈ 𝑅3
U = SPAN
2
3
1
-1
0
1,
U is sub space on 𝑅3
s
33.
34. VECTOR = MAGNITUDE + DIRECTION
5 mph East
Speed
Scalar
Velocity = Vector
I am sure that you
got that