Important: The linalg package has been deprecated. Use the superseding command LinearAlgebra[Transpose], instead.

- For information on migrating linalg code to the new packages, see examples/LinearAlgebraMigration.

The matrix transpose of A is computed.  The result is an n x m matrix. The [i,j]th element of the result is equal to the [j,i]th element of A. The result inherits the indexing function (for example, diagonal or sparse) of A, if it has one.

If A is a vector, then it is treated as if it were a column vector; transpose(A) would therefore be a row vector.

The command with(linalg,transpose) allows the use of the abbreviated form of this command.

$\mathrm{with}\left(\mathrm{linalg}\right)\:$

$A≔\mathrm{array}\left(\left[\left[1\,2\,3\right]\,\left[4\,5\right]\right]\right)$

$A≔\left[\begin{array}{ccc}1& 2& 3\\ 4& 5& {\mathrm{`?`}}_{2,3}\end{array}\right]$

$\mathrm{transpose}\left(A\right)$

$\left[\begin{array}{cc}1& 4\\ 2& 5\\ 3& A_{2,3}\end{array}\right]$

$B≔\mathrm{array}\left(\mathrm{diagonal}\,1..2\,1..2\,\left[\left(1\,1\right)=5\right]\right)$

$B≔\left[\begin{array}{cc}5& 0\\ 0& {\mathrm{`?`}}_{2,2}\end{array}\right]$

$\mathrm{transpose}\left(B\right)$

$\left[\begin{array}{cc}5& 0\\ 0& B_{2,2}\end{array}\right]$

$C≔\mathrm{array}\left(\left[1\,2\,3\right]\right)$

$C≔\left[\begin{array}{ccc}1& 2& 3\end{array}\right]$

$\mathrm{Ct}≔\mathrm{transpose}\left(C\right)$

$\mathrm{Ct}≔\mathrm{transpose}\left(C\right)$

$\mathrm{evalm}\left(C\&*\mathrm{Ct}\right)$

$\left[\begin{array}{ccc}1& 2& 3\\ 2& 4& 6\\ 3& 6& 9\end{array}\right]$

$\mathrm{evalm}\left(\mathrm{Ct}\&*C\right)$

$14$