# Define Matrix Order with Examples? and Types of Matrix Order in Math

## History of Matrix Order

The idea of matrices was introduced by a famous mathematician Arther Cayley in 1857. Matrices are widely used in both physical and social science. In this article we will introduce a new mathematical form, called a matrix, that will enable us to represent a number of different qualities as a single unit.

### Details of Matrix:

Before going to know about the Matrix order we can briefly understand matrices. A matrix is a rectangular array of any number or function. Matrices are 2-dimensional .it is represented by rows and columns. Rows are denoted by m and columns are denoted by n. Now we move towards matrix order. The term matrix order is defined as multiply the number of rows and columns in that matrix. We write the order of the matrix in such a manner that the number of rows first show  and then the number of columns.

## What is Matrix order in math?

A matrix is a square or a rectangular array of numbers written within square brackets or parentheses in a definite order, in rows and columns. The term matrix order is defined as the number of rows and columns in that matrix. for example

Generally, the matrices (plural of the matrix) are denoted by capital letters… A, B, C………….etc. while the elements of a matrix are denoted by small letters a, b, c…………. and numbers 1, 2, 3,……..

### Easy Matrix Order Example:

A=\begin{bmatrix}3&5\\5&1\end{bmatrix} ,

B=\begin{bmatrix}2&3&2\\2&2&1\\4&3&4\end{bmatrix} ,

C=\begin{bmatrix}1\\2\end{bmatrix} ,

D=\begin{bmatrix}1&2\end{bmatrix}

We write the order of matrix in such a manner that number of row first show  and then the number of columns

Example

Let suppose a matrix A has m number of row and n number of the column then the order of the matrix is m*n

Let A be matrix

A=\begin{bmatrix}1&2&2\\1&2&0\end{bmatrix}

Here are 2 rows and 3 columns So order of matrix A is 2*3.

### Types of Matrix in Maths

Some important types of matrix order are as follow:

### Define Row matrix with Examples

The matrix having only one row is called a row matrix.

Examples:

Example No 1.

A=\begin{bmatrix}1&2&3\end{bmatrix}

The order of this matrix is 1×3

Example No 2.

B=\begin{bmatrix}1&2&3&4&5\end{bmatrix}

.Order of this matrix is 1×5

### Define Column matrix with Examples

The matrix having only one column is called a column matrix.

Examples:

Example No 1.

A=\begin{bmatrix}1\\2\\3\end{bmatrix}

Order of this matrix is 3×1

Example No 2.

B=\begin{bmatrix}1\\2\\3\\4\end{bmatrix}

Order of this matrix is 4×1

### Define Null Matrix with Examples

A matrix in which all entries are zero is called a null matrix.

Examples:

Example No 1.

A=\begin{bmatrix}0&0&0\\0&0&0\\0&0&0\end{bmatrix}

Order of this matrix is 3×3

Example No 2.

B=\begin{bmatrix}0&0&0\\0&0&0\end{bmatrix}

Order of this matrix is 2×3

### Explain Square matrix with Examples

A matrix in which a number of rows and number of columns are equal is called a square matrix.

Examples:

Example No 1.

A=\begin{bmatrix}1&2&3\\4&5&6\\7&8&9\end{bmatrix}

Order of this matrix is 3×3

Example No 2.

B=\begin{bmatrix}1&2\\3&4\end{bmatrix}

Order of this matrix is 2×2

### Definition of Diagonal matrix with Easy Examples

A square matrix in which diagonals entries are non-zero and off-diagonals entries are zero is called a diagonals matrix

Examples:

Example No 1.

A=\begin{bmatrix}1&0&0\\0&2&0\\0&0&2\end{bmatrix}

Order of this matrix is 3×3

Example no 2.

B=\begin{bmatrix}1&0\\0&2\end{bmatrix}

Order of this matrix is 2×2

### Define Upper triangular matrix with Examples in Math

A square matrix in which all entries below the main diagonals are zero is called upper triangular matrix.

Examples:

Example No 1.

A=\begin{bmatrix}1&2&2\\0&2&2\\0&0&5\end{bmatrix}

order of this matrix is 3-by-3

Example No 2.

B=\begin{bmatrix}1&1\\0&1\end{bmatrix}

Order of this matrix is 2-by-2

The upper triangular matrix must be a square matrix.

### Lower triangular matrix with Examples

A square matrix in which all items overhead the main diagonals are zero is called a lower triangular matrix.

Examples:

Example No 1.

A=\begin{bmatrix}1&0&0\\1&2&0\\2&2&2\end{bmatrix}

Order of this matrix is 3-by-3

B=\begin{bmatrix}1&0&0&\\4&6&0&0\\4&4&5&0\\2&5&4&1\end{bmatrix}

The order of this matrix is 4-by- 4

A lower triangular matrix is also must be a square matrix.

### What is Symmetric matrix in Math?

A square matrix in which its transpose is equal to itself is called a symmetric matrix