The horner function writes the polynomial M in horner or nested form.

The horner(M) calling sequence converts all elements of M to horner form.  The result, R, is formed as R[i,j] = horner(M[i,j]).

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

$M≔\mathrm{Matrix}\left(2\,3\,'\mathrm{fill}'=x^3-6x^2+11x-6\right)\:$

$\mathrm{horner}\left(M\right)$

$\left[\begin{array}{ccc}-6+\left(11+\left(-6+x\right)x\right)x& -6+\left(11+\left(-6+x\right)x\right)x& -6+\left(11+\left(-6+x\right)x\right)x\\ -6+\left(11+\left(-6+x\right)x\right)x& -6+\left(11+\left(-6+x\right)x\right)x& -6+\left(11+\left(-6+x\right)x\right)x\end{array}\right]$