Transpose - Maple Help

LinearAlgebra[Modular]

 Transpose
 compute the transpose of a mod m Matrix or Vector

 Calling Sequence Transpose(m, A, inplace)

Parameters

 m - modulus A - mod m Matrix or Vector inplace - (optional) keyword for inplace operation on square Matrix

Description

 • 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](..).

Examples

 > $\mathrm{with}\left(\mathrm{LinearAlgebra}\left[\mathrm{Modular}\right]\right):$
 > $p≔97$
 ${p}{≔}{97}$ (1)
 > $M≔\mathrm{Mod}\left(p,\mathrm{Matrix}\left(3,4,\left(i,j\right)↦\mathrm{rand}\left(\right)\right),\mathrm{integer}\left[\right]\right)$
 ${M}{≔}\left[\begin{array}{cccc}{77}& {96}& {10}& {86}\\ {58}& {36}& {80}& {22}\\ {44}& {39}& {60}& {39}\end{array}\right]$ (2)
 > $\mathrm{Transpose}\left(p,M\right)$
 $\left[\begin{array}{ccc}{77}& {58}& {44}\\ {96}& {36}& {39}\\ {10}& {80}& {60}\\ {86}& {22}& {39}\end{array}\right]$ (3)
 > $\mathrm{V1}≔\mathrm{Mod}\left(p,\mathrm{Vector}\left[\mathrm{row}\right]\left(3,i↦\mathrm{rand}\left(\right)\right),\mathrm{float}\left[8\right]\right)$
 ${\mathrm{V1}}{≔}\left[\begin{array}{ccc}{43.}& {12.}& {55.}\end{array}\right]$ (4)
 > $\mathrm{Transpose}\left(p,\mathrm{V1}\right)$
 $\left[\begin{array}{c}{43.}\\ {12.}\\ {55.}\end{array}\right]$ (5)
 > $\mathrm{V2}≔\mathrm{Mod}\left(p,\mathrm{Vector}\left[\mathrm{column}\right]\left(3,i↦\mathrm{rand}\left(\right)\right),\mathrm{float}\left[8\right]\right)$
 ${\mathrm{V2}}{≔}\left[\begin{array}{c}{2.}\\ {24.}\\ {71.}\end{array}\right]$ (6)
 > $\mathrm{Transpose}\left(p,\mathrm{V2}\right)$
 $\left[\begin{array}{ccc}{2.}& {24.}& {71.}\end{array}\right]$ (7)
 > $\mathrm{Copy}\left(p,\mathrm{V2},'\mathrm{transpose}'\right)$
 $\left[\begin{array}{ccc}{2.}& {24.}& {71.}\end{array}\right]$ (8)
 > $\mathrm{Multiply}\left(p,\mathrm{Transpose}\left(p,\mathrm{V2}\right),\mathrm{V2}\right)$
 ${92.}$ (9)
 > $M≔\mathrm{Create}\left(p,3,3,\mathrm{random},\mathrm{integer}\right)$
 ${M}{≔}\left[\begin{array}{ccc}{43}& {8}& {76}\\ {58}& {15}& {0}\\ {69}& {76}& {38}\end{array}\right]$ (10)
 > $\mathrm{Transpose}\left(p,M,\mathrm{inplace}\right):$
 > $M$
 $\left[\begin{array}{ccc}{43}& {58}& {69}\\ {8}& {15}& {76}\\ {76}& {0}& {38}\end{array}\right]$ (11)