Tensor T. Linear Transformation

**vercammen** · December 20th 2012, 06:54 AM

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 $\mathbb{R}^m$

**xxp9** · December 20th 2012, 11:12 AM

$S^*(T)(x) = T(S(x))=T(Bx)=A(Bx)=(AB)x$

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