Matrix Transpose

Transpose of Matrix

The matrix obtained by interchanging the rows and columns of a matrix is called transpose of the matrix.

If A is the original matrix, then the transpose if denoted as A’ or A^T

Example 1:

For the following matrix A, find the transpose of A.

Solution:

Here is the transpose matrix after changing rows and columns :

Example 2:

Find the transpose of the following matrices.

Solution:

Common Rules of Matrix Transpose

• (A + B) ‘ = A’ + B ‘
• (A’)’ = A
• (A B) ‘ = B’ A’
• (c A) ‘ = c A’ , here c is a constant

Symmetric and Skew-symmetric matrix

A square matrix A is symmetric, if A = A’

A square matrix A is skew-symmetric, if A = -A’

Example:

Solution:

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