# Tensor T. Linear Transformation

• Dec 20th 2012, 07:54 AM
vercammen
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 $\mathbb{R}^m$
• Dec 20th 2012, 12:12 PM
xxp9
Re: Tensor T. Linear Transformation
$S^*(T)(x) = T(S(x))=T(Bx)=A(Bx)=(AB)x$