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The Transpose(L) function transposes a list of lists as if it were a matrix.

Note: Within a procedure, it is likely that changing the indices is more efficient than creating a new transposed list of lists. Therefore, procedure Transpose should only be used for modifying lists of lists that need to be returned in transposed form.

In the special case where the argument is of type $\mathrm{list}\left(\left[\right]\right)$, $\left[\left[\right]\right]$ is returned.

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

$L≔\left[\left[1\,2\,3\right]\,\left[a\,b\,c\right]\,\left[X\,Y\,Z\right]\right]$

$L≔\left[\left[1\,2\,3\right]\,\left[a\,b\,c\right]\,\left[X\,Y\,Z\right]\right]$

$L\left[1,2\right]$

$2$

$L\left[2,1\right]$

$a$

$R≔\mathrm{Transpose}\left(L\right)$

$R≔\left[\left[1\,a\,X\right]\,\left[2\,b\,Y\right]\,\left[3\,c\,Z\right]\right]$

$R\left[1,2\right]$

$a$

$\mathrm{Transpose}\left(\left[\left[\right]\,\left[\right]\,\left[\right]\right]\right)$