# transpose(Matrix) -- transpose a matrix

## Synopsis

• Function: transpose
• Usage:
transpose f
• Inputs:
• f,
• Outputs:
• , the transpose of f

## Description

Here is an example.
 i1 : S = ZZ/10007[x,y,z]; i2 : f = matrix{{x^3,x*y^2},{y*x^2,y^3}} o2 = | x3 xy2 | | x2y y3 | 2 2 o2 : Matrix S <--- S i3 : g = transpose f o3 = {-3} | x3 x2y | {-3} | xy2 y3 | 2 2 o3 : Matrix S <--- S
The output of transpose is a map between the duals of the original source and target free modules. See:
 i4 : degrees f o4 = {{{0}, {0}}, {{3}, {3}}} o4 : List i5 : degrees g o5 = {{{-3}, {-3}}, {{0}, {0}}} o5 : List

## Caveat

transpose works only for maps between free modules. Use dual for more general maps.