List questions from multilinear-algebra

Published on 19 Jul 2017 - 6:23

205

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Differences between linear functions, multi-linear functions and morphisms.

Published on 27 Mar 2026 - 12:34

18.6k

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Cross product in higher dimensions

Published on 29 Mar 2026 - 15:20

92

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This shows up in algebraic topology, right?

Published on 26 Jul 2017 - 9:16

274

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Is there a name for the "two-argument" Gramian matrix?

Published on 29 Mar 2026 - 14:29

620

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Hodge Star basis-independence proof

Published on 30 Jul 2017 - 17:10

75

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How to prove $\dim ( \hom(V_1, ..., V_p ; U) ) =\dim(V_1) \cdot .... \cdot \dim(V_p) \cdot \dim(U)$ by induction?

Published on 05 Aug 2017 - 11:19

122

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Is there a reasonable generalization of the formula $|x\times y|^2+|x\bullet y|^2 = |x|^2|y|^2$ to higher dimensions?

Published on 29 Mar 2026 - 14:35

554

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Generalization of matrix for multilinear maps

Published on 17 Aug 2017 - 23:15

78

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Derivative of tensor function of single variable

Published on 29 Mar 2026 - 14:28

119

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The very first appearance of concept of a Tensor.

Published on 24 Aug 2017 - 9:13

38

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Is every $k$-form $\omega$ on $V\oplus W$ of the form $\omega=\sum_{i+j=k} \pi_V^\alpha_i\wedge \pi_W^ \beta_j$?

Published on 24 Aug 2017 - 13:43

402

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Triple cross product formula using multilinear algebra

Published on 29 Mar 2026 - 14:28

132

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Are some specific multilinear functions other than bilinear forms studied?

Published on 26 Aug 2017 - 17:43

568

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How do I know that these definitions of inner product of $k$-vectors and Hodge star are well-defined?

Published on 31 Aug 2017 - 9:39

List Question

Range of a bilinear mapping spans codomain

Differences between linear functions, multi-linear functions and morphisms.

Cross product in higher dimensions

This shows up in algebraic topology, right?

Is there a name for the "two-argument" Gramian matrix?

Hodge Star basis-independence proof

How to prove $\dim ( \hom(V_1, ..., V_p ; U) ) =\dim(V_1) \cdot .... \cdot \dim(V_p) \cdot \dim(U)$ by induction?

Is there a reasonable generalization of the formula $|x\times y|^2+|x\bullet y|^2 = |x|^2|y|^2$ to higher dimensions?

Generalization of matrix for multilinear maps

Derivative of tensor function of single variable

The very first appearance of concept of a Tensor.

Is every $k$-form $\omega$ on $V\oplus W$ of the form $\omega=\sum_{i+j=k} \pi_V^\alpha_i\wedge \pi_W^ \beta_j$?

Triple cross product formula using multilinear algebra

Are some specific multilinear functions other than bilinear forms studied?

How do I know that these definitions of inner product of $k$-vectors and Hodge star are well-defined?

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