MATRIX UNIT -1

Date:13/12/2023

Reg no:23UCM001

                   Matrix

         Matrix is a rectangular table or array of symbols, numbers or expressions, arranged in columns and rows. The dimension of a matrix is 2x3 or below, as there are two rows and three columns.

 

Types of Matrices

Matrices can be classified into many broad categories, based on the number of rows, columns, and many other factors.

 

                           Row Matrix

A matrix with a single row is considered to be a row matrix.  In the cases where m = 1, A = [aij]mxn.  Row matrix has only one row and the order of a row matrix is 1 x n.  Example: In the row matrix of order 1 x 4, A = [ 1 2 4 5]  In the row matrix of order 1 x 3, P = [ -4 -21 -17]                            Ex:                     A = [aij]1×n                     Column Matrix        A matrix with one column is considered a column matrix. In A = [aij]mxn, the column matrix is n = 1 column matrix                                          Ex:                            A = [aij]m×1                 ZERO or NULL MATRIX       A zero matrix is a matrix that has all its elements equal to zero. Since a zero matrix contains only zeros as its elements, therefore, it is also called a null matrix. A zero matrix can be a square matrix. A zero matrix is denoted by 'O'               Ex:

                

                      SQUARE MATRIX 

      A square matrix is an n × n matrix; that is, a matrix having the same number of rows as columns.

                  Ex:

 

                         SCALAR  MATRIX

          The diagonal elements of the scalar matrix are equal or same. If the elements of the scalar matrix are all equal is called

Scalar matrix

                         Ex:

                                   A=                  

                        DIOGNAL MATRIX

        A square matrix in which every element except the principal diagonal elements is zero is called a Diagonal Matrix. 

                Ex:

                                   A=

                            UNIT MATRIX 

       A Square Matrix whose DIOGNAL elements are unit, Each and non diognal

elements are zero is called unit matrix

                   Ex:

                                   I=

           

                     SYMMETRIC MATRIX 

         A Square Matrix such that aii =aij  I and j is called a symmetric matrix

                     Ex:

                               A=

                    SKEW -SYMMETRIC

             A Square matrix A is said to be skew-symmetric if aij =−aji for all i and j.

                                  A=

                  ORTHOGONAL MATRIX 

           A square Matrix A is said to be an orthogonal Matrix. 

                    Ex:

                           If AIA=AAI= I

          

                      SINGULAR MATRIX

        

      A square Matrix A is said to be singular Matrix. 

                   Ex:

                          If |A|=0

                         Non-singular

        A square Matrix A is said to be non-singular Matrix. 

                     Ex:

                           If |A|≠0.