Different types of Matrices

Introduction:

                   A rectangular array of entries is called a Matrix. The entries may be real, complex or functions. The entries are also called as the elements of the matrix. The rectangular array of entries are enclosed in an ordinary bracket or in square bracket.

Types of Matrices:

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.

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.......a_nn is called the principal diagonal or the leading diagonal.
The elements a₁₁, a₂₂,.......a_nn are called the diagonal elements of the square matrix.

Diagonal Matrix:

A square matrix A=[a_ij]_nxn is called a diagonal matrix if all the elements, except those in the leading diagonal, are zero.
i.e., a_ij = 0 for all i j

Scalar Matrix:

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

Identity or Unit Matrix:

A square matrix A=[a_ij]_{n x n} is called an identity or unit matrix if

(2) a_ij =1 for all i = j
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.

Hope you liked the above explanation. Please leave your comments, if you have any doubts.