Matrices: Definition and Classification 

DEFINITION

A rectangular array of symbols (which could be real or complex numbers) along rows and columns is called a matrix.

Thus a system m × n symbols arranged in a rectangular formation along m rows and n columns and bounded by the brackets [.] is called an m by n matrix (which is written as m x n matrix)

i.e. A =  is a matrix of order m × n.

In a compact form the above matrix is represented by A = [a_ij], 1 < i < m,
1 < j < n, where is, j ε i or simply [a_ij] m × n.

The numbers a₁₁, a₁₂, ... etc of this rectangular array are called the elements of the matrix. The element a_ij belongs to the i^th row and the j^th column and is called the (i, j)^th element of the matrix.

Equal Matrices

Two matrices are said to be equal if they have the same order and each element of one is equal to the corresponding element of the other.

CLASSIFICATION OF MATRICES

Row Matrix

A matrix having a single row is called a row matrix. e.g. [1 3, 5, 7]

Column Matrix

_{A matrix having a single column is called a column matrix. e.g.}.

Square Matrix

An m x n matrix A is said to be a square matrix if m = n i.e. number of rows = number of columns.

For example:    A = is a square matrix of order 3 × 3.

Note: In a square matrix the diagonal from left hand side upper corner to right hand side lower corner is known as leading diagonal or principal diagonal. In the above example square matrix containing the elements 1, 3, 5 is called the leading or principal diagonal.