There are different types of Matrices. Here they are -

1) Row matrix

2) Column matrix

3) Null matrix

4) Square matrix

5) Diagonal matrix

6) Upper triangular matrix

7) Lower triangular matrix

8) Symmetric matrix

9) Skew -symmetric matrix

10) Horizontal matrix

11) Vertical matrix

12) Identity matrix

Let's discuss the different types of matrices in mathematics, types of matrix in detail, matrices definition and types.

1. **Null Matrix**

If in a matrix all the elements are zero then it is called a zero matrix and it is generally denoted by 0. Thus, is a zero-matrix if for all and .

The first matrix is a matrix with all the elements equal to zero and the second matrix is a matrix with all the elements equal to zero.

2. Triangular Matrix

A square matrix is known to be triangular if all of its elements above the principal diagonal are zero then the triangular matrix is known as a lower triangular matrix or all of its elements below the principal diagonal are zero then the triangular matrix is known as upper triangular matrix.

The matrix given above is a upper triangular matrix.

The matrix given below is an example of a lower triangular matrix.

3. Vertical Matrix

A matrix of order is known as a vertical matrix of , where is equal to the number of rows and is equal to the number of columns.

Matrix Example

In the matrix example given below the number of rows , whereas the number of columns Therefore, this makes the matrix a vertical matrix.

4. Horizontal Matrix

A matrix of order is known as a horizontal matrix if , where is equal to the number of rows and is equal to the number of columns.

Matrix Example

In the matrix example given below the number of rows (m) = 2, whereas the number of columns (n) = 4. Therefore, we can say that the matrix is a horizontal matrix.

5. Row Matrix

A matrix that has only one row is known as a row matrix. Thus A = aijm×n is a row matrix if m is equal to 1.

It is known so because it has only one row and the order of a row matrix will hence always be equal to .

Example of a Row matrix,

In the matrix example given above, matrix A has only one row and so matrix B has one row, therefore both matrices A and B are row matrices.

6. Column Matrix

A matrix that has one column is known as a Column matrix. Thus A = aijm×n is a column matrix if n is equal to 1.

It is known so because it has only one column and the order of a column matrix will hence always be equal to m×1

Example of a Column matrix,

In the matrix example given above, matrix A has only one column and matrix B has one column, therefore both matrices A and B are column matrices.

7. Diagonal Matrix

If all the elements of the matrix, except the principal diagonal in any given square matrix, is equal to zero, it is known as a diagonal matrix. Thus a square matrix A = aij

is a diagonal matrix if , when is not equal to

For example,

The example given above is a diagonal matrix as it has elements only in its diagonal.

8. Symmetric Matrix

A square matrix is known as a Symmetric matrix if , for all i,j values.

For example,

9. Skew -Symmetric Matrix

A square matrix is a skew-symmetric matrix if , for all values of i,j. Thus, in a skew-symmetric matrix all diagonal elements are equal to zero.

For example,

10. Identity Matrix

If all the elements of a principal diagonal in a diagonal matrix are 1 , then it is called a unit matrix. A unit matrix of order can be denoted by . Thus, a square matrix

is an identity matrix if all its diagonals have value 1.