# Types of Matrix

**Quadratic Matrix**is a matrix whose number of rows is equal to the number of columns.

**The zero matrix**is a matrix with all entries equal to zero

Matrix properties zero:

A
+ 0 = A (if the size of the matrix A = matrix size 0)

A0
= 0; 0A = 0 (if multiplication requirements are met)

**The Diagonal Matrix**is a quadratic matrix where all of the entries outside the main diagonal are zero.

**Identity Matrix or Unit Matrix**is a diagonal matrix whose main diagonal entries are all numbers 1. The ordinary identity matrix is written I or I

_{n}where

*n*shows the size (order) of the quadratic matrix.

The nature of the identity matrix is like the number 1 (one) in operations with ordinary numbers, namely:

AI = A; IA = A (if conditions are met)

**Example 1**

Then,

**The lower triangular matrix**is a quadratic matrix with all entries above diagonal = 0.

**An upper triangular matrix**is a quadratic matrix in which all the entries below the main diagonal = 0

**Symmetrical Matrix**is a matrix whose transposes are the same as themselves, in other words if A = A

^{t}.

Because
A = A

^{t}., Then A is a symmetrical matrix.**Antisymmetric Matrix**is a matrix whose transposes are negative or A

^{t}= - A. It is easy to understand that all the main diagonal entries of the antisymmetric matrix are 0.

Because
A

^{t}= - A, the matrix A is an antisymmetric matrix.**Commutative Matrix**

If A and B are squared
metrics and apply AB = BA, then A and B are said to be communicative with each
other. It is clear that each commutative square I (which is the same
size) and with its inverse (if any). If AB = -BA, it is said to be
anticomutative.alau AB = -BA, dikatakan antikomutatif.

**Idempotent Matrix, Periodic, Nilpoten**

The quadratic matrix A is
said to apply the bile

**Idempotent Matrix**AA = A^{2}= A. Generally if*p*is the smallest (positive round) number, so AA applies ... A = A^{p}= A, then it is said A**Periodic Matrix**with period (p - 1) . If Nilpoten A is A^{t}= 0 for an natural number*r*it is said A is nilpotent with index*r*. The Matrix Index is the smallest positive integer*r*that satisfies the A^{r}= 0 relationship.
Because,

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