Transpose of a Matrix

The transpose of a matrix is one of the most common methods used for matrix transformation in matrix concepts across linear algebra.

Definition

The transpose of a matrix is obtained by interchanging its rows into columns or columns into rows. The transpose of the matrix is denoted by using the letter $T$ in the superscript of the given matrix. For example, if $A$ is the given matrix, then the transpose of the matrix is represented by $A^{'}$ or$A^{T}$.

Transpose of a matrix

$A={\begin{bmatrix}a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{23}\end{bmatrix}}_{2\times 3}$ $A^{T}={\begin{bmatrix}a_{11}&a_{21}\\a_{12}&a_{22}\\a_{13}&a_{23}\end{bmatrix}}_{3\times 2}$