Matrix Basic Definitions

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Matrix Definitions

Square Matrix :

Any matrix that has equal number of rows and columns is called square matrix. E.g: 2x2, 3x3 matrix.

2x2 Square Matrix 3x3 Square Matrix
a11a12
a21a22
2 rows & 2 columns
b11b12b13
b21b22b23
b31b32b33
3 rows & 3 columns
Diagonal Matrix :

A Diagonal matrix is a square matrix with numbers on the leading diagonal and zeros in all other places.

Diagonal Matrix
200
030
008
Identity Matrix :

An identity matrix is a square matrix denoted as I. It has ones (1) down the leading diagonal and zeros in all other places.

2x2 identity 3x3 identity
10
01
100
010
001

Note: Any matrix multiplied by its identity matrix leaves the matrix unchanged. It is similar to multiplying a number by 1. i.e AI = A (where A is a matrix)

22
53
x
10
01
=
22
53
Zero (Null) Matrix :

A zero or null matrix is a matrix with 0 as the element for all its cells (rows and columns).

Zero (null) Matrix
000
000
000
Symmetric Matrix :

A symmetric matrix is a matrix where aij = aji. i.e an element at the ith row, jth columns should be equal to the element at the jth row, ith columns.

Symmetric Matrix
123
245
356
Equality Matrix :

For any two matrices to be said as equal matrices they should be of same size and have same values.

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