Introduction
- To find the Transpose Matrix we have to interchange the rows and columns
- That is, the 1st row becomes the 1st column, the 2nd row becomes the second column, 3rd row becomes the 3rd column.
- Notation: If A is the original matrix, the transpose of A will be denoted as ATor Ã.
The following examples shows how to find the Transpose of a Matrix
\[\Large
A =
\begin{bmatrix}
\color{red}{1} & \color{red}{2} \\
\color{blue}{3} & \color{blue}{4}
\end{bmatrix}
\qquad
A^T =
\begin{bmatrix}
\color{red}{1} & \color{blue}{3} \\
\color{red}{2} & \color{blue}{4}
\end{bmatrix}
\]
\[\Large B = \begin{bmatrix} \color{red}{1} & \color{red}{2} & \color{red}{3} \\ \color{blue}{4} & \color{blue}{5} & \color{blue}{6} \\ \color{green}{7} & \color{green}{8} & \color{green}{9} \end{bmatrix} \qquad B^T = \begin{bmatrix} \color{red}{1} & \color{blue}{4} & \color{green}{7} \\ \color{red}{2} & \color{blue}{5} & \color{green}{8} \\ \color{red}{3} & \color{blue}{6} & \color{green}{9} \end{bmatrix} \]
\[\Large C = \begin{bmatrix} \color{red}{5} & \color{red}{6} & \color{red}{7} \end{bmatrix} \qquad C^T = \begin{bmatrix} \color{red}{5} \\ \color{red}{6} \\ \color{red}{7} \end{bmatrix} \]
\[\Large B = \begin{bmatrix} \color{red}{1} & \color{red}{2} & \color{red}{3} \\ \color{blue}{4} & \color{blue}{5} & \color{blue}{6} \\ \color{green}{7} & \color{green}{8} & \color{green}{9} \end{bmatrix} \qquad B^T = \begin{bmatrix} \color{red}{1} & \color{blue}{4} & \color{green}{7} \\ \color{red}{2} & \color{blue}{5} & \color{green}{8} \\ \color{red}{3} & \color{blue}{6} & \color{green}{9} \end{bmatrix} \]
\[\Large C = \begin{bmatrix} \color{red}{5} & \color{red}{6} & \color{red}{7} \end{bmatrix} \qquad C^T = \begin{bmatrix} \color{red}{5} \\ \color{red}{6} \\ \color{red}{7} \end{bmatrix} \]
What is the transpose of a matrix?