# Tensor T. Linear Transformation

Let $T$ be a $1-$tensor on $\mathbb{R}^n$;
then $T(y) = A \cdot y$for some matrix $A$of size $1 \times n$.
If $S:\mathbb{R}^m \rightarrow \mathbb{R}^n$is a linear transformation $S(x)= B \cdot x$,
what is the matrix of the $1-$tensor $S^* (T)$on $\mathbb{R}^m$
$S^*(T)(x) = T(S(x))=T(Bx)=A(Bx)=(AB)x$