It contains the basics of matrix which includes matrix definition,types of matrices,operations on matrices,transpose of matrix,symmetric and skew symmetric matrix,invertible matrix,
application of matrix.
It contains the basics of matrix which includes matrix definition,types of matrices,operations on matrices,transpose of matrix,symmetric and skew symmetric matrix,invertible matrix,
application of matrix.
Some types of matrices, Eigen value , Eigen vector, Cayley- Hamilton Theorem & applications, Properties of Eigen values, Orthogonal matrix , Pairwise orthogonal, orthogonal transformation of symmetric matrix, denationalization of a matrix by orthogonal transformation (or) orthogonal deduction, Quadratic form and Canonical form , conversion from Quadratic to Canonical form, Order, Index Signature, Nature of canonical form.
Matrix is the structure squares of information science. They show up in different symbols across dialects. From Numpy clusters in Python to data frames in R, to lattices in MATLAB. The Matrix in its most essential structure is an assortment of numbers masterminded in a rectangular or cluster like the style
The following presentation consists of information about the application of matrices. The ppt particularly focuses on the its use in cryptography i.e. encoding and decoding of messages.
Some types of matrices, Eigen value , Eigen vector, Cayley- Hamilton Theorem & applications, Properties of Eigen values, Orthogonal matrix , Pairwise orthogonal, orthogonal transformation of symmetric matrix, denationalization of a matrix by orthogonal transformation (or) orthogonal deduction, Quadratic form and Canonical form , conversion from Quadratic to Canonical form, Order, Index Signature, Nature of canonical form.
Matrix is the structure squares of information science. They show up in different symbols across dialects. From Numpy clusters in Python to data frames in R, to lattices in MATLAB. The Matrix in its most essential structure is an assortment of numbers masterminded in a rectangular or cluster like the style
The following presentation consists of information about the application of matrices. The ppt particularly focuses on the its use in cryptography i.e. encoding and decoding of messages.
Matrix theory" redirects here. For the physics topic, see Matrix string theory.
An m × n matrix: the m rows are horizontal and the n columns are vertical. Each element of a matrix is often denoted by a variable with two subscripts. For example, a2,1 represents the element at the second row and first column of the matrix.
In mathematics, a matrix (plural matrices) is a rectangular array[1] (see irregular matrix) of numbers, symbols, or expressions, arranged in rows and columns.[2][3] For example, the dimension of the matrix below is 2 × 3 (read "two by three"), because there are two rows and three columns:
{\displaystyle {\begin{bmatrix}1&9&-13\\20&5&-6\end{bmatrix}}.}{\displaystyle {\begin{bmatrix}1&9&-13\\20&5&-6\end{bmatrix}}.}
Provided that they have the same size (each matrix has the same number of rows and the same number of columns as the other), two matrices can be added or subtracted element by element (see conformable matrix). The rule for matrix multiplication, however, is that two matrices can be multiplied only when the number of columns in the first equals the number of rows in the second (i.e., the inner dimensions are the same, n for an (m×n)-matrix times an (n×p)-matrix, resulting in an (m×p)-matrix). There is no product the other way round, a first hint that matrix multiplication is not commutative. Any matrix can be multiplied element-wise by a scalar from its associated field.
Chemistry in our daily life and its importanceAMIR HASSAN
Chemistry in our daily life and its importance
A Short Introduction to Chemistry and its branches.
There are five main branches of Chemistry:
1)Organic Chemistry
2)Inorganic Chemistry
3)Analytical Chemistry
4)Physical Chemistry
5)Biochemistry
Presented By: Amir Hassan Chemistry Department, Government Post Graduate College Mardan KP Pakistan.
Difference Between Environmental Science and Environmental ChemistryAMIR HASSAN
Environmental chemistry is the scientific study of the chemical and biochemical phenomena that occur in natural places.
Environmental science deals with ecosystem maintenance; by using the combined knowledge of the science fields that include the area of physics, geography, astro, biology and chemistry.
Environmental Science & Environmental Chemistry in
Contamination and Pollution
Environmental Science & Environmental Chemistry in
The Atmosphere
Environmental Science & Environmental Chemistry in
The water
Environmental Science & Environmental Chemistry in
The Soil and Rocks
Environmental Science & Environmental Chemistry in
The Trace Toxics
The Haworth Projection or, RepresentationAMIR HASSAN
The Fischer projection does not accurately describe the shape of the cyclic hemiacetal form of D – Glucose (as shown in figure A).
A formulation suggested by the English chemist W.N. Haworth in which ring are written as flat or, planar hexagons is more correct
A simple way of drawing Haworth projection is to omit the ring carbon. Thus α – D – glucose and β – D – glucose may be represented as shown;
Chemistry of Natural Products
Alkaloids
• Introduction; classification; isolation; general methods for structure elucidation; discussion with particular reference to structure and synthesis of ephedrine, nicotine, atropine, quinine, papaverine and morphine.
• Terpenoids
• Introduction; classification; isolation; general methods for structure elucidation; discussion with particular reference to structure and synthesis of citral, α-terpineol, α-pinene, camphor and α-cadinene.
• Steroids
• Introduction; nomenclature and stereochemistry of steroids; structure determination of cholesterol and bile acids; introduction to steroidal hormones with particular reference to adrenal cortical hormones.
Detection Of Free Radical By Different Methods
1. Magnetic Susceptibility Measurement.
2. ESR ( Electron Spin Resonance) Technique.
3. Spin Trapping Technique.
4. NMR (Nuclear magnetic resonance) Spectra by CIDNP effect.
5. X-Ray Technique
Soil,Soil Pollution, Sources of Soil Pollution,
Effects Of Soil Pollution,
Control Of Soil Pollution,
Physically Control of Soil Pollution,
Chemically Control of Soil Pollution,
Thermally Control of Soil Pollution ,
Biologically Control of Soil Pollution
Introducation to organo metallic compund or grignard reagentAMIR HASSAN
Introducation to organo metallic compund or grignard reagent, structure, prepration, physical and chemical properties, types of chemical reaction, applications, by AMIR HASSAN FROM GPGC MARDAN, KPK, PAKISTAN.
Neighboring group participation, mechanism, groups, consequencesAMIR HASSAN
Neighboring group participation, mechanism, groups, consequences (FROM ORGANIC CHEMISTRY) by AMIR HASSAN OF GOVT. POST GRADUATE COLLAGE MARDAN, KPK, PAKISTAN.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
For more information, visit-www.vavaclasses.com
How to Split Bills in the Odoo 17 POS ModuleCeline George
Bills have a main role in point of sale procedure. It will help to track sales, handling payments and giving receipts to customers. Bill splitting also has an important role in POS. For example, If some friends come together for dinner and if they want to divide the bill then it is possible by POS bill splitting. This slide will show how to split bills in odoo 17 POS.
Model Attribute Check Company Auto PropertyCeline George
In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
Ethnobotany and Ethnopharmacology:
Ethnobotany in herbal drug evaluation,
Impact of Ethnobotany in traditional medicine,
New development in herbals,
Bio-prospecting tools for drug discovery,
Role of Ethnopharmacology in drug evaluation,
Reverse Pharmacology.
Students, digital devices and success - Andreas Schleicher - 27 May 2024..pptxEduSkills OECD
Andreas Schleicher presents at the OECD webinar ‘Digital devices in schools: detrimental distraction or secret to success?’ on 27 May 2024. The presentation was based on findings from PISA 2022 results and the webinar helped launch the PISA in Focus ‘Managing screen time: How to protect and equip students against distraction’ https://www.oecd-ilibrary.org/education/managing-screen-time_7c225af4-en and the OECD Education Policy Perspective ‘Students, digital devices and success’ can be found here - https://oe.cd/il/5yV
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.
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
1. WrittenBy : AMIR HASSAN OFBS CHEMISTRY DEPARTMENT GPGC MARDAN
INTRODUCATION TO MATRICES
CONCEPTOF MATRIX:
The concept of matrices was first prevented by Arther Kelley,
an eminent mathematician, in the middle of 19th century, and its use in different scientific
disciplines has since been increasing day by day.
MATRICES IN CHEMISTRY:
1) Any symmetry operation about a symmetry element in a molecule involves the
transformation of a set of coordinates x, y and z of an atom into a set of new coordinates
x`, y` and z`.
2) The two sets of coordinates of the atom can be related by a set of equations. This set of
equations may also be formulated in matrix notation.
3) Thus each symmetry operation can be represented by a specific matrix.
4) Knowledge of the matrices of various operations in a molecule will be useful to solve
structural problems in chemistry.
5) For Example: The symmetry of vibrational modes in molecules can be analyzed using
the matrices for different operation.
MATRIX:-
A matrix is a rectangular array of numbers or symbol for numbers
arranged in rows and columns.
i. In mathematical terms, Matrices (plural of matrix) are rectangular or, square tables whose
elements are written in order in the form of rows and columns.
ii. Matrices are usually represented by the capital letters of English alphabets i.e. A, B, C, D, E…
and their numbers are shown by small letters of English alphabets i.e. a, b, c, d, e…
iii. Horizontal entries in matrix are called its Rows, (denoted by i).
iv. While vertical entries are called its columns, (denoted by j).
v. Though it is not necessary that a matrix should have equal number of rows and columns, but it is
necessary that number of members in different rows or columns should be equal.
vi. For example: if the numbers in members in the first row of a matrix is 3 then the numbers of
elements in all other rows will be 3. Similarly if there are 2 elements in first column of a matrix
then all other columns of the same matrix will also have 2 elements.
A= B= C= D= E= F= G=
1 -2
3 4
a b
c d
5 7
x
y
0 a
aij bij
cij dij
2. WrittenBy : AMIR HASSAN OFBS CHEMISTRY DEPARTMENT GPGC MARDAN
ORDER OR, DIMENSIONOF A MATRIX:-
Numbers of rows and columns in a matrix represent the order or dimension of a matrix.
For Example: if the number of rows in a matrix is m and the number of columns be n then order
or dimension of matrix will be m × n.
Remember that order m × n does not mean the product of “m” and “n”. It’s read as “m by n”.
i.e. order ofmatrix = no. ofrows × no. of columns
A= and B= no. of rows is 2 × no. ofcolumn is also 2.
Hence order ofmatrices A and B is 2 × 2.
C= no. of rows is 1 × no. of column is 2. D= no. of rows is 2× no. of column is 1.
Hence order of matrix C is 1 × 2. Hence order of matrix D is 2 × 1.
KINDS OF A MATRICES:-
1) ROW MATRIX:
A matrix consist of only one row and n column is called row matrix.
Examples are the following:
A= order is 1 × 4. B= order is 1 × 1.
2) COLUMN MATRIX:
A matrix consists of only one column and m rows is called column matrix.
Examples are the following :
A= order is 2 × 1. B= order is 2 × 1.
C= order is 1 × 1.
3) SQUARE MATRIX: A matrix in which the numbers of rows is equal to the number of
column is called square matrix.
Examples are the following:
A= order is 2 × 2. B= order is 2 × 2. C= order is 1 × 1.
4) RECTANGULAR MATRIX: A matrix in which the numbers of rows is not equal to
the number of column is called square matrix.
A= no. of rows is 2 × no. of column is 1. D= no. of rows is 1× no. of column is 2.
1 -2
3 4
a b
c d
5 7 x
y
22 5 9 4
6 7
5
7
x
y
2
1 -2
3 4
a b
c d
2
5 7
x
y
3. WrittenBy : AMIR HASSAN OFBS CHEMISTRY DEPARTMENT GPGC MARDAN
5) DIAGONAL MATRIX: A square matrix in which all the elements is zero “0”, except its
diagonal elements is called diagonal matrix.
Consider a square matrix elements a11,a22,a33,called its diagonal elements.
A= M= N= R=
6) UNIT OR IDENTITYMATRIX:
“A square matrix in which their diagonal element is equal to one (w.r.t multiplication) and every
non diagonal element is equal to zero is called diagonal matrix”.
It is usually denoted by I. Example are the following
I= I= I=
7) ZERO/NULL MATRIX: A square or, rectangular matrix in which their all the element is
equal to zero is called zero or null matrix.
- It is usually denoted by letter “O” of English alphabet. Examples are the following
O= O= O= O=
8) SCALAR MATRIX: A square matrix in which the diagonal elements are the same is
called scalar matrix.
- Examples are the following
A= B= C=
9) NEGATIVE OF MATRIX:
- “If the signs of all the elements of a matrix are changed then new matrix are formed is called
negative of the matrix or, additive inverse of the matrix”.
Examples are the following
A= then -A=
a11 a12 a13
a21 a22 a23
a31 a32 a33
1 0
0 1
x 0
0 y
-1 0
0 4
1 0
0 1
1
1 0 0
0 1 0
0 0 1
0 0 0
0
0
0 0
0 0
0
2 0
0 2
-5 0
0 -5
1 0
0 1
2 -3
6 -1
-2 3
-6 1
4. WrittenBy : AMIR HASSAN OFBS CHEMISTRY DEPARTMENT GPGC MARDAN
10) TRANSPOSEOF MATRIX: The transpose of a matrix is obtained by interchanging its
rows and columns are called transpose of the matrix.
-It is usually denoted by At
or Ã. If the order of matrix is m × n new matrix obtained order
is n × m called transpose of the matrix. Example are the following
IF A = then At
or à = B= Bt
=
11) ADJOINT OF MATRIX: The adjoint of a matrix is obtained by interchanging the
principle diagonal elements positions and the signs of the second diagonal elements.
A= Adj. A= A= Adj. A=
12) DETERMINANTOF MATRIX: The determinant of a matrix is obtained by
multiplying the principal diagonal elements and subtracts the second diagonal elements.
- The determinant of matrix contains exactly the same elements as its real matrix. The only
difference is that of the elements of matrix are written inside a square bracket while in case of
determinants two vertical line segments ׀׀ used instead of brackets.
A= then, ׀A׀ = ׀A׀ = ad – bc
13) SINGULAR & NON SINGULAR MATRIX: If the value of determinant of square
matrix is zero called singular matrix or not equal to zero known as non singular matrix.
A= then ׀A=׀ ׀A =׀ 2 × 8 – 4 × 4 = 16 – 16
=0 (is singular matrix)
B= then ׀B=׀ ׀ B =׀ 1 × 4 – 2 × 3 = 4 – 6
= – 2 ≠ 0 (is non singular matrix)
-5 -7
2 1
-5 2
-7 1
9
7
9 7
a b
c d
d -b
-c a
6 -3
4 -2
-2 3
-4 6
a b
c d
a b
c d
2 4
4 8
2 4
4 8
1 2
3 4
1 2
3 4