## What is periodic matrix?

A square matrix such that the matrix power for a positive integer is called a periodic matrix. If is the least such integer, then the matrix is said to have period .

## How do you find the periodicity of a matrix?

Periodic Matrix – Definition and Example

- Example : Find the period of the matrix A = [ 1 − 2 − 6 − 3 2 9 2 0 − 3 ] .
- A = [ 1 − 2 − 6 − 3 2 9 2 0 − 3 ] .
- = [ 5 − 6 − 6 9 10 9 − 4 − 4 − 3 ] .
- ⟹ A 3 =
- = [ 1 − 2 − 6 − 3 2 9 2 0 − 3 ] = A.

**What is the period of idempotent matrix?**

An idempotent matrix is one which, when multiplied by itself, doesn’t change. If a matrix A is idempotent, A2 = A.

### What is idempotent matrix with example?

Idempotent matrix is a square matrix, which multiplied by itself, gives back the initial square matrix. A matrix M, when multiplied with itself, gives back the same matrix M, M2 = M. Let us consider a matrix A = (abcd) ( a b c d ) . Further since A is taken as an idempotent matrix, we have A2 = A.

### What are the types of matrix?

This tutorial is divided into 6 parts to cover the main types of matrices; they are:

- Square Matrix.
- Symmetric Matrix.
- Triangular Matrix.
- Diagonal Matrix.
- Identity Matrix.
- Orthogonal Matrix.

**What is equal matrix?**

Two matrices are called equal matrices if they have the same order or dimension and the corresponding elements are equal. Suppose A and B are the matrices of equal order i × j and aij = bij, then A are B are called equal matrices.

#### What is a periodic Markov chain?

A state in a Markov chain is periodic if the chain can return to the state only at multiples of some integer larger than 1. Periodic behavior complicates the study of the limiting behavior of the chain.

#### What is meant by Involutory Matrix?

In mathematics, an involutory matrix is a square matrix that is its own inverse. That is, multiplication by the matrix A is an involution if and only if A2 = I, where I is the n × n identity matrix. Involutory matrices are all square roots of the identity matrix.

**What is nilpotent and idempotent matrix?**

Idempotent means “the second power of A (and hence every higher integer power) is equal to A”. Nilpotent means “some power of A is equal to the zero matrix”.

## What are the 4 types of matrices?

Tutorial Overview

- Square Matrix.
- Symmetric Matrix.
- Triangular Matrix.
- Diagonal Matrix.
- Identity Matrix.
- Orthogonal Matrix.

## What is matrix formula?

A matrix equation is an equation of the form Ax = b , where A is an m × n matrix, b is a vector in R m , and x is a vector whose coefficients x 1 , x 2 ,…, x n are unknown.