Types of Matrices


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Row Matrix

A matrix having only one row is called a row-matrix.

For example: A[1 3 2 -2] is a row matrix of order 1 x 4.

Column Matrix

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

3 x 1 and 4 x 1 respectively.

Square Matrix

A matrix in which the number of rows is equal to the number of columns, say n, is called a square matrix of order n.

In this square matrix of order n the elements a11, a22.......ann is called the principal diagonal or the leading diagonal.

The elements a11, a22,.......ann are called the diagonal elements of the square matrix.

The leading diagonal elements are 2, -2 and -3.

Diagonal Matrix

A square matrix A=[aij]nxn is called a diagonal matrix if all the elements, except those in the leading diagonal, are zero.

i.e., aij = 0 for all i j

Example:

Scalar Matrix

A scalar matrix is a diagonal matrix in which all the diagonal elements are equal.

Example:

The matrices  are scalar matrices of order 2 and 3 respectively.

Identity or Unit Matrix

A square matrix A=[aij]n x n is called an identity or unit matrix if

(2) aij =1 for all i = j

In other words a square matrix each of whose diagonal elements is unity and each of whose non-diagonal elements is equal to zero is called an identity or unit matrix. The identity matrix of order n is denoted by In.

Example:

The matrices  are identify matrices of order 2 and 3 respectively.

Null Matrix or Zero Matrix

A matrix of order m x n whose elements are all 0 is called a null matrix (or zero matrix) of order m x n. It is usually denoted by O or more clearly [O]m,n.

Example:

 are all zero matrices of orders 1 x 2, 2 x 1, 2 x 2 and 3 x 3 respectively.



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