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Thread: Tensor T. Linear Transformation

  1. #1
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    Tensor T. Linear Transformation

    Let $\displaystyle T$ be a $\displaystyle 1-$tensor on $\displaystyle \mathbb{R}^n$;
    then $\displaystyle T(y) = A \cdot y$for some matrix $\displaystyle A$of size $\displaystyle 1 \times n$.

    If $\displaystyle S:\mathbb{R}^m \rightarrow \mathbb{R}^n$is a linear transformation $\displaystyle S(x)= B \cdot x$,
    what is the matrix of the $\displaystyle 1-$tensor $\displaystyle S^* (T)$on $\displaystyle \mathbb{R}^m$
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  2. #2
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    Re: Tensor T. Linear Transformation

    $\displaystyle S^*(T)(x) = T(S(x))=T(Bx)=A(Bx)=(AB)x$
    Thanks from vercammen
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