Matrix and it's types

[ Matrix ]

A set of mn numbers in the form of m horizontal lines and n vertical lines, is called an order of mxn Matrix or rectangular matrix

Types of Matrices 

Idempotent Matrix

A matrix which is multiply by itself and give the same matrix.

If satisfy above condition then A is Idempotent Matrix.

Involutary Matrix

A matrix A which is multiply by itself and give Identity Matrix.

Nilpotent Matrix

A matrix is called Nilpotent Matrix.

where k is a positive integer, k is least positive integer and k is called as the index of the nilpotent matrix.

Periodic Matrix

for periodic matrix we have,

where k is least positive integer.

Orthogonal Matrix

A square matrix A is called orthogonal matrix if