Matrices

Matrices

A matrix, designated by a bold capital letter, is a collection of elements enclosed in brackets in the form of rectangular array with horizontal rows and vertical columns. A matrix is usually denoted by a upper case letter and an element of matrix is often denoted by a lower case letter with double subscript notation

The matrix A is of order m x n with m rows and n columns.

Row i of the matrix: ;

Column j of the matrix:

Element is the matrix content at the intersection of row i and column j.

Square Matrix

A matrix with the same number of rows as columns, m = n is called a square matrix of order n.

Principal Diagonal

The elements where i = j forms the principal diagonal of a square matrix.

Trace

The trace of a square matrix is the sum of the elements on the principal diagonal.

Vector

For a single row matrix, of order 1 x n, it is called a row vector or row matrix.

For a single column matrix, of order m x 1, it is called a column vector or column matrix.

A vector is usually represented by a lower case letter, e.g. a

Zero Matrix

If a matrix of any order consists all elements zero, it is called a zero matrix or null matrix, O.

Equality of Matrices,

Let and ,

if two matrices are of the same order, & and the corresponding elements are equal, , then two matrices are equal,