Definition of a Matrix

DEFINITION 1.1.1 (Matrix)   A rectangular array of numbers is called a matrix.

We shall mostly be concerned with matrices having real numbers as entries.

The horizontal arrays of a matrix are called its ROWS and the vertical arrays are called its COLUMNS. A matrix having rows and columns is said to have the order

A matrix of ORDER can be represented in the following form:

where is the entry at the intersection of the row and column.

In a more concise manner, we also denote the matrix by by suppressing its order.

Remark 1.1.2   Some books also use to represent a matrix.

Let Then and

A matrix having only one column is called a COLUMN VECTOR; and a matrix with only one row is called a ROW VECTOR.

WHENEVER A VECTOR IS USED, IT SHOULD BE UNDERSTOOD FROM THE CONTEXT WHETHER IT IS A ROW VECTOR OR A COLUMN VECTOR.

DEFINITION 1.1.3 (Equality of two Matrices)   Two matrices and having the same order are equal if for each and

In other words, two matrices are said to be equal if they have the same order and their corresponding entries are equal.

EXAMPLE 1.1.4   The linear system of equations and can be identified with the matrix

Subsections
A K Lal 2007-09-12