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Transpose of a Matrix

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Description

The transpose of a matrix can be defined as a new matrix whose rows are the columns of the original matrix and the columns are the rows of the original matrix. If A is a matrix then its transpose is denoted as $A^{T}$ .

For example:

If a matrix is:

Then the transpose of the matrix is

Algorithm

INPUT: A matrix
OUTPUT: The transpose of the matrix

PROCESS:
Step 1: [taking the input]
	Read m, n [the 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: [The transpose of the matrix]
	for i = 0 to m-1 repeat
        		for j = 0 to n-1 repeat
        			Set t[j][i]<-a[i][j]
		[End of ‘for loop]
	[End of ‘for’ loop]
	[printing the transpose matrix]
	Print "The transpose of the matrix is:"
	For i=0 to n-1 repeat
		For j=0 to m-1 repeat
			Print t[i][j]
			If j=m-1 then
				Move to the next line
			[End of ‘if’]
		[End of ‘for’ loop]
	[End of ‘for’ loop]
Step 3: Stop.

Code

TIME COMPLEXITY:

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

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

{ t[j][i]=a[i][j];

}

//printing the transpose matrix

printf("\nThe transpose of the matrix is:\n");

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

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

{ printf("%d ",t[i][j]);

if(j==m-1)------- O(c1)

printf("\n");

}

The time complexity is O(m*n). if the number of rows and columns are equal, then the time complexity is O( $n^{2}$ ).

APPLICATION:

The transpose of a matrix is used to flip a matrix over its diagonal.

Contributed by

Souvick Das

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