List questions from multilinear-algebra

Published on 14 Oct 2017 - 15:41

40

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Show that $\tau \sum_{\sigma \in S_k} f = \sum_{\sigma \in S_k} \sigma f$

Published on 15 Oct 2017 - 4:17

1.1k

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Two definitions of the tensor product and their relation

Published on 19 Oct 2017 - 10:59

709

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Alternative definition for tensor product which nowhere occurs (to my knowledge)

Published on 19 Oct 2017 - 12:08

245

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Show that the set of all multilinear maps is a subspace

Published on 23 Oct 2017 - 2:15

214

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Antisymmetry of exterior product for alternating multilinear forms

Published on 29 Mar 2026 - 19:11

985

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Wedge product of vectors and of linear functionals

Published on 29 Mar 2026 - 17:25

107

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$i_a = (i_b + i_c + 1)/2$ and $f(x) = f(x - f(x-1)) /2$?

Published on 27 Mar 2026 - 4:35

114

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Why in this theorem the field of characteristic equal to $2$ excluded?

Published on 06 Nov 2017 - 13:27

2.7k

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Diagonalizability of symmetric bilinear forms over fields of characteristic $2$

Published on 29 Mar 2026 - 13:47

168

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Show that the pair $(\varphi, \mbox{Hom}(V^*,W))$ is a tensor product to $V,W$.

Published on 09 Nov 2017 - 17:38

82

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Construction of tensor product to $V_1,\cdots, V_k$

Published on 10 Nov 2017 - 11:21

177

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Tensor identity: $(E_1\otimes F) \cap (E_2 \otimes F) = (E_1\cap E_2)\otimes F.$

Published on 12 Nov 2017 - 13:24

233

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What's the connection between a field, vector, matrix and higher-order tensors?

Published on 13 Nov 2017 - 16:49

1.4k

Views

Determinant construction by exterior algebra and vector space orientations

Published on 14 Nov 2017 - 1:28

List Question

Introduction to complex tensor algebra

Show that $\tau \sum_{\sigma \in S_k} f = \sum_{\sigma \in S_k} \sigma f$

Two definitions of the tensor product and their relation

Alternative definition for tensor product which nowhere occurs (to my knowledge)

Show that the set of all multilinear maps is a subspace

Antisymmetry of exterior product for alternating multilinear forms

Wedge product of vectors and of linear functionals

$i_a = (i_b + i_c + 1)/2$ and $f(x) = f(x - f(x-1)) /2$?

Why in this theorem the field of characteristic equal to $2$ excluded?

Diagonalizability of symmetric bilinear forms over fields of characteristic $2$

Show that the pair $(\varphi, \mbox{Hom}(V^*,W))$ is a tensor product to $V,W$.

Construction of tensor product to $V_1,\cdots, V_k$

Tensor identity: $(E_1\otimes F) \cap (E_2 \otimes F) = (E_1\cap E_2)\otimes F.$

What's the connection between a field, vector, matrix and higher-order tensors?

Determinant construction by exterior algebra and vector space orientations

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