Definition of a matrix | Improve Society

A matrix of order m × n, or m by n matrix, is a rectangular array of numbers having m rows and n columns. It can be written in the form

$A = \left( \begin{array}{ccccc} a_{11} & a_{12} & a_{13} & \cdots & a_{1n} \\ a_{21} & a_{22} & a_{23} & \cdots & a_{2n} \\ \cdots & \cdots & \cdots & \cdots & \cdots \\ a_{m1} & a_{m2} & a_{3m} & \cdots & a_{mn} \end{array} \right)\cdots(1)$

Each number $a_{jk}$ in this matrix is called an element. The subscripts $j$ and $k$ indicate respectively the row and column of the matrix in which the element appears.

We shall often denote a matrix by a letter, such as $A$ in (1), or by the symbol $(a_{jk})$ which shows a representative element.

A matrix having only one row is called a row matrix or row vector while a matrix having only one column is called a column matrix or column vector. If the number of rows $m$ and columns $n$ are equal the matrix is called a square matrix of order $n \times n$ or briefly $n$ . A matrix is said to be a real matrix or complex matrix according as its elements are real or complex numbers.