# Tensor T. Linear Transformation

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• December 20th 2012, 06:54 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 $\mathbb{R}^m$
• December 20th 2012, 11:12 AM
xxp9
Re: Tensor T. Linear Transformation
$S^*(T)(x) = T(S(x))=T(Bx)=A(Bx)=(AB)x$