Sciences, Technology & Medicine

## Matrices

The bookÂ 'Matrices'Â has been written in an innovative style. This book is a complete treatise on Real Mathematics portion, matrices, which also serves a vital role in Mathematical Physics and various other scientific fields. This book contains subject matter in an explicit, lucid and comprehensive manner. It identifies an essential framework which will be helpful to students giving their respective universities graduate and postgraduate exams, as well as serves with its straightforward and modern approach to the subject concept which will be of great help for the students appearing in different Engineering competitive exams. A number of simple and depictive illustrations are given along with large number of solved and unsolved examples.
• Publisher: Laxmi Publications
• Language: English
• ISBN : 978-81-318-0702-6
• Chapter 1

### Introduction to Matrices Price 2.99  |  2.99 Rewards Points

A matrix is rectangular array of scalars i.e., all those numbers that obey the algebraic laws of addition, subtraction, multiplication and division. The system of numbers, arranged in rectangular array is in rows and columns and bounded by brackets. Normally, this array is enclosed within square brackets. [ ], sometimes parenthesis ( ) or otherwise double vertical bars || are used.
• Chapter 2

### Some Special Type Of Matrices Price 2.99  |  2.99 Rewards Points

The matrix which is obtained by interchanging the rows and columns of a given matrix A is called transpose of matrix, denoted by A or AT.
• Chapter 3

### Elementary Transformation Price 2.99  |  2.99 Rewards Points

The following three operations are required to be called elementary operation/transformation for any given matrix : (a) interchange of any two rows [columns] (b) multiplication of row/column by any non-zero scalar. (c) addition to one row/column of another row/column multiplied by any non-zero scalar. All these operations (a), (b) and (c) are called elementary transformation. So, an elementary transformation is called an elementary row transformation or an elementary column transformation according as it applies to rows or columns.
• Chapter 4

### Rank Of Matrix Price 2.99  |  2.99 Rewards Points

Let A be matrix of order m  n. So, the determinant of the square submatrix of order is called a minor of A of order k. From any given matrix, we can form a square submatrix of order 1, 2, 3, ....., m if m < n or of order 1, 2, 3, ....., n if n < m.
• Chapter 5

### Simultaneous Equations Price 2.99  |  2.99 Rewards Points

Simultaneous Equations
• Chapter 6

### Linear Dependance Of Vectors Price 2.99  |  2.99 Rewards Points

Any two numbers x, y can be presented in two different ways : 1. first x and then y 2. first y and then x. Also this presentation can be represented as (x, y) or (y, x) depending upon the order of writing the two numbers x and y. This (x, y) is called as ordered pair here in (x, y) x is first member and y is second member.
• Chapter 7

### Charecteristic Roots and Charecteric Vectors Price 2.99  |  2.99 Rewards Points

Any equation of the form A0 + A1 x + A2 x2 + ...... + An xn = 0, where A0, A1, ....., An are square matrices of same order and An  0. So such polynomial is called matrix polynomial of n degree.
• Chapter 8

### Cayley Hamilton Theorem Price 2.99  |  2.99 Rewards Points

Any equation of type | A â€“ I | = 0 is called as characteristic equation of A.
• Chapter 9

### Diagonalisation of Matrices Price 2.99  |  2.99 Rewards Points

Any two square matrices A and B, having same order (say n) are said to be similar if there exists a non-singular matrix P such that B = Pâ€“1 AP. Here B is said to be similar to A.
• Chapter 10

### Matrices Determinants Price 2.99  |  2.99 Rewards Points

A rectangular array of scalars that consists of all those numbers that obey algebraic laws of addition, subtraction, multiplication and division. In other words, matrix is defined as set of mn numbers which are arranged in rectangular array having m rows and n vertical columns, called as (m  n) type matrix.