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Checking of Square Matrix

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Description

A square matrix in which all the elements of the principal diagonal are 1, and all other elements are 0, then this matrix is known as identity matrix.

 

For example:

Algorithm

INPUT: A matrix
OUTPUT: whether it is an identity matrix or not

PROCESS:
Step 1: [taking the input]
	Read m, n [number of rows and columns of the matrix]
	For i=0 to m-1 repeat
		For j=0 to n-1 repeat
			Read a[i][j]
		[End of ‘for’ loop]
	[End of ‘for’ loop]
Step 2: [Checking for identity matrix]
	for i = 0 to m-1 repeat
		for j = 0 to n-1 repeat
			if i = j and a[i][j]≠1 then
				Set f <- 1
				break
			else if  i ≠ j and a[i][j] ≠ 0 then
				Set f <- 1
				break
			[End of ‘if’]
		[End of ‘for’ loop]
	[End of ‘for’ loop]
	If f=0 then
		Print "The matrix is an identity matrix"
	else
		print "The matrix is not an identity matrix"
	[End of ‘if’]
Step 3: Stop.

Code

TIME COMPLEXITY:

for (i = 0; i < m; i++)--------------- O(m)

                {     for (j = 0; j < n; j++)------------ O(n)

                                {    if (i == j && a[i][j] != 1)----- O(c1)

                                                {             f = 1;

                                                                break;   }

                                                else if (i != j && a[i][j] != 0)------- O(c2)

                                                {              f = 1;

                                                                break;   }

                }

The complexity is O(m*n). as the matrix is a square matrix therefore, the value of m and n should be the same. Therefore, the complexity is O(n2).

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