The function Map(f,M1,...,Mn) applies the function f to each element of M1, with extra arguments M2,...,Mn.

The function Map[k](f,M1,...,Mn) applies the function f to each element of Mk, with extra arguments M1,...,Mk-1,Mk+1,...,Mn.

For scalar Mk, the function Map[k](f,M1,...,Mn) is equivalent to f(M1,...,Mn).

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

$M≔\mathrm{Matrix}\left(\left[\left[1\,2\right]\,\left[3\,4\right]\right]\right)\:$

$\mathrm{Map}\left(a\mapsto a^2\,M\right)$

$\left[\begin{array}{cc}1& 4\\ 9& 16\end{array}\right]$

$\mathrm{Map}\left(a\mapsto a^2\,b+c\right)$

${\left(b+c\right)}^2$

$\mathrm{Map}\left[2\right]\left(\mathrm{`+`}\,a\,\left[b\,c\right]\,d\right)$

$\left[a+b+d\,a+c+d\right]$