Matrix theory

Matrix theory

Definitions:-
1.) Matrix: - A matrix is defined as rectangular array or arrangement of numbers subjected to some rules of operations. Thus rectangular array of ‘mn’ numbers in m rows and n columns is called m×n matrix and is read as ‘m by n’ matrix.


Example: - [ 1 7 6 9 ]
Above example shows that given matrix has one row m=1 and four columns n=4
2.) Order of matrix:- Total number of rows and columns in a given matrix define its order e.g. in above matrix order is 1×4.
3.) Square matrix and rectangular matrix:- A matrix in which the number of rows is equal to number of columns is called a square matrix i.e. m=n in case of square matrix.
E.g. a matrix of order 1×1, 2×2, 3×3 etc.
A matrix for which number of rows is not equal to number of columns is known as rectangular matrix.
E.g. a matrix of order 2×3, 3×4, 2×1 etc.are the examples of rectangular matrix.
4.) Diagonal elements: - The elements aij of the matrix A= [aij] m×n for which i=j are called the diagonal elements
5.) Diagonal matrix: - A square matrix in which all the non diagonal elements are equal to zero ,is called diagonal matrix .following example shows diagonal matrix of 3×3 order
6.) Scalar matrix: - A diagonal matrix, in which all the diagonal elements are equal, is called a scalar matrix.
e.g:-
7.) Unit matrix (identity matrix):- A scalar matrix each of whose diagonal elements is unity is called a unit or identity matrix .It is generally denoted by I.
e.g:- I=
8.) Null matrix: - If all the elements in a matrix are equal to zero, the matrix is called a null matrix or zero matrix.
e.g:-
0 =
9.) Column matrix: - A matrix which contain only a single column is called a column matrix
E.g.:- A matrix of 3×1 order
10.) Row matrix: - A matrix which contains only a single row is called a row matrix, e.g.:- a matrix of order 1× 2 is example of row matrix
[2 5]
11.) Upper triangular matrix: - A square matrix A= [aij] is called upper triangular matrix, if aij=0, for i>j
e.g:-
A =


12.) Lower triangular matrix: - A square matrix A= [aij] is called lower triangular matrix, if aij=0, for i

Student of Rai Business School - New Delhi

Sanjeev Kumar Singh