# Definition

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

Thus, a system of

*m*Ã—*n*symbols arranged in a rectangular formation along*m*rows and*n*columns and bonded by the brackets [â‹…] is called an*m*by*n*matrix (which is written as*m*Ã—*n*matrix). Thus,*A*= is a matrix of order

*m*Ã—

*n*.

In a compact form the above matrix is represented by

*A*= [*a*], 1 â‰¤_{ij}*i*â‰¤*m*, 1 â‰¤*j*â‰¤*n*or simply [*a*]_{ij}_{m}_{Ã—n}. The numbers*a*_{11},*a*_{12}, â€¦, etc. of this rectangular array are called the elements of the matrix. The element*a*belongs to the_{ij}*i*th row and*j*th column and is called the (*i*,*j*)th element of a matrix.