3.5 Types of Matrices:
Definitions:
‘Square Matrix’ is a matrix whose number of rows are same as number of columns.
Square matrix’s order is represented by m (m x m) 

A= order :3X3 B= order: 2X2 
The
Principal diagonal elements (from top left corner to bottom right corner) of
matrix A are {1,5,9} The
Principal diagonal elements (from top left corner to bottom right corner) of
matrix A are {1,4} 

A=_{} order :3X2 B=_{} order :2X3 
Note
Matrix A is 3X2 and Matrix B is 2X3 Since
these two are not square matrices, we cannot identify their diagonal
elements. 

A matrix whose principal diagonal
elements are non zero and all other elements are zero is called ‘Diagonal matrix.’ 

A=Principal
diagonal elements are {2,4,6} B= Principal
diagonal elements are {2,4,6} 
Observe
that in both A and B except for diagonal elements all other elements are
zero. 

A ‘Scalar matrix’ is a diagonal matrix whose principal
diagonal elements are equal 

A= Principal
diagonal elements are {2,2,2} B= Principal
diagonal elements are {5,5} 


An ‘Identity matrix’ is a diagonal matrix
whose principal diagonal elements are 1. 

A=Principal
diagonal elements are {1,1,1} B= Principal
diagonal elements are {1,1} 


‘Symmetric matrix’ is a square matrix whose elements are symmetric (same) with respect
to principal diagonal elements. (Mirror
copy with respect to principal diagonal). 

A=_{}Principal diagonal elements are {5, 9,6} B= _{}Principal diagonal elements are {7, 9} 
Notice
that in A the elements on both the sides of principal diagonal are same {2,2},{4,4},{6,6}. Notice
that in B the elements on both the sides of principal diagonal are same {2,2}. 

Skew symmetric matrix’ is a square matrix whose elements are symmetric with respect to the
principal diagonal with opposite sign and principal diagonal elements are
zero 

A=_{}Principal diagonal elements are {0,0,0} B= _{}Principal diagonal elements are {0,0} 
Notice
that in A the elements on both the sides of principal diagonal are same with
opposite sign {2,2},{4,4},{6,6}.) Notice
that in B the elements on both the sides of principal diagonal are same with
opposite sign {2,2}.) 

A=_{} order 1X4 B=_{} order 1X2 
Row matrix’ is a matrix which has only one row and is of the order (1 x n) 

A=_{} order: 4X1 B=_{} order : 2X1 
‘Column matrix’ is a
matrix which has only one column and is of order (m x 1) 

A=_{} order 3X4 B=_{} order 2X3 
‘Zero matrix’ is a matrix whose elements are all zeros. It need
not be a square matrix 

A=_{} B= _{} Then A=B 
Two
matrices are said to be ‘equal’ if and only if they are of same order and
corresponding elements are equal. 
A=_{} B = _{} If
A=B, then 
a=1,
b=2,c=3,d=4,e=5,f=6,g=7,h=8,i=9,j=2,k=4,l=6.
Rows Columns 
‘Transpose of a matrix’ is obtained by converting elements of rows
in to columns and elements of columns in to rows. Transpose of A is denoted by A^{1}. 

A= _{} order 4X3 A^{1}= _{} order 3X4 
Rows: {2,4,6},{8,9,1},{3,5,7},{2,4,6}. Columns: {2,8,3,2},{4,9,5,4},{6,1,7,6} Rows: {2,8,3,2},{4,9,5,4},{6,1,7,6}. Columns: {2,4,6},{8,9,1},{3,5,7},{2,4,6} 
3.5
Summary of learning
No 
Points
studied 
1 2 
Types of matrices  Square matrix, rectangular
matrix, diagonal matrix, Symmetric matrix, Zero matrix, Skew matrix, Identity
matrix Transpose of a matrix 