TYPES OF MATRICES

Types of matrices :

Here we are going to see different types of matrix with detailed examples.

Row matrix :

A matrix which is having only one row is called row matrix.

Examples:

 5 -2 7 9

 a b c

The order of first row matrix is 1 x 4

The order of second row matrix is 1 x 3

Column matrix :

A matrix which is having only one column is called column matrix.

 1 -2 0

The order of the above column matrix is 3 x 1

 a b

The order of the above column matrix is 2 x 1

Square matrix :

A square matrix is a matrix in which the number of rows and the number of columns are equal. A matrix of order n x n is also known as a square matrix of order n.

In a square matrix A of the order n x n the elements a11,a22,a33........ann is called principal diagonal or leading diagonal or main diagonal elements.

 3 2 1 -5 0 11 -3 2 8

The order of the above square matrix is 3 x 3.

Diagonal matrix

In a diagonal matrix all the entries except the entries along the main diagonal are zero.

 4 0 0 0 5 0 0 0 6

Triangular matrix

A square matrix is known as a lower triangular matrix if all elements above main diagonal are zero .

 3 2 1 0 5 3 0 0 1

A square matrix is known as a upper triangular matrix if all elements below main diagonal are zero .

 3 0 0 5 8 0 1 -2 5

Scalar matrix :

A square matrix is known as a scalar matrix if all the entries along the main diagonal are equal.

 3 0 0 3

Identity (or) scalar matrix

When all the entries along the main diagonal are equal to 1 is known as identity matrix or unit matrix. Usually identity matrix is denoted by I₂ if the order of that particular matrix is 2 x 2 and it is denoted by I₃ if the order of that particular matrix is 3 x 3.

 1 0 0 1

 1 0 0 0 1 0 0 0 1

Zero matrix (or) null matrix (or) void matrix :

In a matrix if all the entries are zero then it is called zero matrix.

 0 0 0 0

 0 0 0 0 0 0 0 0 0

Equality of matrices :

Two matrices A and B are known as equality of matrices if both matrices is having same order. These are the types of matrices.

Transpose of matrix :

A matrix formed by interchanging rows as columns and columns as rows is called as transpose of a matrix. The transpose of matrix A is usually denoted by A^T

If A =

 1 5 7 2 3 8

then AT =

 1 2 5 3 7 8

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