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Math Help - Tensor T. Linear Transformation

  1. #1
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    Tensor T. Linear Transformation

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

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

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