The Transpose function returns the transpose of the input mod m Matrix or Vector.

It uses the more flexible mod m Copy function to compute the transpose.

If A is a square Matrix, the transpose can be performed in-place.

This command is part of the LinearAlgebra[Modular] package, so it can be used in the form Transpose(..) only after executing the command with(LinearAlgebra[Modular]).  However, it can always be used in the form LinearAlgebra[Modular][Transpose](..).

$\mathrm{with}\left({\mathrm{LinearAlgebra}}_{\mathrm{Modular}}\right)\:$

$p≔97$

$p≔97$

$M≔\mathrm{Mod}\left(p\,\mathrm{Matrix}\left(3\,4\,\left(i\,j\right)\→\mathrm{rand}\left(\right)\right)\,{\mathrm{integer}}_{\[\]}\right)$

$M≔\left[\begin{array}{cccc}77& 96& 10& 86\\ 58& 36& 80& 22\\ 44& 39& 60& 39\end{array}\right]$

$\mathrm{Transpose}\left(p\,M\right)$

$\left[\begin{array}{ccc}77& 58& 44\\ 96& 36& 39\\ 10& 80& 60\\ 86& 22& 39\end{array}\right]$

$\mathrm{V1}≔\mathrm{Mod}\left(p\,{\mathrm{Vector}}_{\mathrm{row}}\left(3\,i\→\mathrm{rand}\left(\right)\right)\,{\mathrm{float}}_8\right)$

$\mathrm{V1}≔\left[\begin{array}{ccc}43.& 12.& 55.\end{array}\right]$

$\mathrm{Transpose}\left(p\,\mathrm{V1}\right)$

$\left[\begin{array}{c}43.\\ 12.\\ 55.\end{array}\right]$

$\mathrm{V2}≔\mathrm{Mod}\left(p\,{\mathrm{Vector}}_{\mathrm{column}}\left(3\,i\→\mathrm{rand}\left(\right)\right)\,{\mathrm{float}}_8\right)$

$\mathrm{V2}≔\left[\begin{array}{c}2.\\ 24.\\ 71.\end{array}\right]$

$\mathrm{Transpose}\left(p\,\mathrm{V2}\right)$

$\left[\begin{array}{ccc}2.& 24.& 71.\end{array}\right]$

$\mathrm{Copy}\left(p\,\mathrm{V2}\,\'\mathrm{transpose}\'\right)$

$\left[\begin{array}{ccc}2.& 24.& 71.\end{array}\right]$

$\mathrm{Multiply}\left(p\,\mathrm{Transpose}\left(p\,\mathrm{V2}\right)\,\mathrm{V2}\right)$

$92.$

$M≔\mathrm{Create}\left(p\,3\,3\,\mathrm{random}\,\mathrm{integer}\right)$

$M≔\left[\begin{array}{ccc}43& 8& 76\\ 58& 15& 0\\ 69& 76& 38\end{array}\right]$

$\mathrm{Transpose}\left(p\,M\,\mathrm{inplace}\right)\:$

$M$

$\left[\begin{array}{ccc}43& 58& 69\\ 8& 15& 76\\ 76& 0& 38\end{array}\right]$