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# Matrix Basic Definitions

## 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
 a11 a12 a21 a22
2 rows & 2 columns
 b11 b12 b13 b21 b22 b23 b31 b32 b33
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
 2 0 0 0 3 0 0 0 8
##### 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
 1 0 0 1
 1 0 0 0 1 0 0 0 1

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)

 2 2 5 3
x
 1 0 0 1
=
 2 2 5 3
##### 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
 0 0 0 0 0 0 0 0 0
##### 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
 1 2 3 2 4 5 3 5 6
##### Equality Matrix :

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