Transpose Matrix Calculator

Matrix Transpose Calculator 

Matrix Transpose Calculator is used to perform a matrix operation which is known as transposition. Transposition is a process in which swapping the rows and columns of a matrix and gives the result in a new matrix where the columns and rows are interchanged.

What is Matrix Transpose?

Transpose of the matrix is a process in which interchange the rows into columns or (columns into the rows) of the given matrix. In other words, if the order of any matrix “A” is “m x n” after processing it becomes “n x m” that is the order of the Transpose Matrix of “A”.

Transpose Matrix Formula:

The Transpose matrix is denoted by “A^t” which is read as the transpose of the matrix “A”. The matrix “A^t” is obtained simply by changing the i^th element of the rows into the j^th element of the column. The general Formula of the Transpose Matrix is defined as.

If A = [a_ij] is a matrix with “m x n” order. Where “i” denotes the i^th rows and “j” denotes the j^th columns.

Then A^t = [a_ji] with the order “n x m” order. Where “j” denotes the j^th rows and “i” denotes the i^th columns after taking the transpose of the matrix.

Examples

Example 1:

Find the transpose matrix of the matrix.

[4   -3   1]

[2   -3   4]

[3   -5   6]

Solution:

Step 1: Let the given matrix be equal to “A”.

A = [4   -3   1]

       [2   -3   4]

       [3   -5   6]

Step 2: The transpose matrix by swapping the rows into columns.

A^t = [4   -3   1]^t

       [2   -3   4]

       [3   -5   6]

A^t = [4  2  3]

       [-3  -3   5]

       [1  4  6]

Example 2:

 Find the Transpose Matrix of the below matrix.

A = [1   -4   2]

       [5   -3   0]

 Solution:

The transpose of the matrix is get by swapping the rows into columns.

A^t = [1   -4   2]^t

       [5   -3   0]

A^t = [1     5]

        [-4   -3]

        [2     0]