Talk:Tensor product: Difference between revisions

Revision as of 23:54, 15 March 2003

Revision as of 01:20, 16 March 2003

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:::i fixed that. looxix, i don't understand what you mean by "giving the example as a tensor prodcut of matrices from which the vector result can be derived easily" - how would i express a tensor with rank>2 without using embedded matrices, which would be potentially confusing? -- [[User:Kevin_baas|Kevin Baas]] -2003.03.15

::::What I meant was an example like:

:::::<math>\begin{bmatrix}a_{11} & a_{12} & a_{13}\\a_{21} & a_{22} & a_{23}\end{bmatrix} \otimes B = \begin{bmatrix}a_{11}B & a_{12}B & a_{13}B\\a_{21}B & a_{22}B & a_{23}B \end{bmatrix} = \dots</math>

::::But this is in fact what is called '''matrix direct product''', sometimes also called '''matrix tensor product'''.

::::What should be better is a general formula such:

:::::<math>A_{ij\dots}^{k\dots} \otimes B_{m\dots}^{npq\dots} = C_{ijm\dots}^{knpq\dots} \Rightarrow c_{ijm\dots}^{knpq\dots} = a_{ij\dots}^{k\dots} \times b_{m\dots}^{npq}