Transpose

The transpose of an m×n matrix is the n×m matrix that you obtain from the first matrix by interchanging the rows and columns.

$\blacktriangleright$ To compute the transpose of a matrix

1.
Place the insertion point in the matrix.

2.
From the Matrices submenu, choose Transpose.

$\blacktriangleright$ Matrices + Transpose

$\left(\vphantom{
\begin{array}{cc}
a & b \\
c & d
\end{array}
}\right.$$\begin{array}{cc}
a & b \\
c & d
\end{array}$$\left.\vphantom{
\begin{array}{cc}
a & b \\
c & d
\end{array}
}\right)$, transpose: $\left(\vphantom{
\begin{array}{cc}
a & c \\
b & d
\end{array}
}\right.$$\begin{array}{cc}
a & c \\
b & d
\end{array}$$\left.\vphantom{
\begin{array}{cc}
a & c \\
b & d
\end{array}
}\right)$

You can also get the transpose of a matrix by using the superscript T.

$\blacktriangleright$ Evaluate

$\left(\vphantom{
\begin{array}{ccc}
a & b & c \\
d & e & f
\end{array}
}\right.$$\begin{array}{ccc}
a & b & c \\
d & e & f
\end{array}$$\left.\vphantom{
\begin{array}{ccc}
a & b & c \\
d & e & f
\end{array}
}\right)^{{T}}_{}$ =  $\left(\vphantom{
\begin{array}{cc}
a & d \\
b & e \\
c & f
\end{array}
}\right.$$\begin{array}{cc}
a & d \\
b & e \\
c & f
\end{array}$$\left.\vphantom{
\begin{array}{cc}
a & d \\
b & e \\
c & f
\end{array}
}\right)$