List questions from multilinear-algebra

Published on 09 Jul 2020 - 14:29

64

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The natural map $V^* \times W \to \text{Hom}(V,W) $ Is bilinear.

Published on 10 Jul 2020 - 11:21

83

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$C(S \times T)$ is isomorphic to $C(S) \otimes C(T).$

Published on 11 Jul 2020 - 17:23

506

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Linear Algebra books that also covers multilinear algebra

Published on 17 Jul 2020 - 3:52

49

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Determinant function theorem

Published on 19 Jul 2020 - 2:29

214

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Prove that $\text{tr} (\phi \otimes \psi) = \text {tr} \phi \text {tr} \psi $.

Published on 22 Jul 2020 - 8:54

28

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$x_{\alpha}\in E$ and $y_{\beta} \in F$ are linearly independent then so are the vectors $\varphi(x_{\alpha},y_{\beta})$ iff $\otimes_2$ holds

Published on 23 Jul 2020 - 2:53

107

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Rank of 3-fold tensor in terms of matrix unfoldings proof

Published on 25 Jul 2020 - 22:32

147

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Is every abstract vector a tensor?

Published on 28 Jul 2020 - 12:36

406

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Is notational compactness in tensors (compared to linear algebra) relevant?

Published on 27 Jul 2020 - 14:29

772

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Exterior algebra of a ring

Published on 12 Jul 2016 - 17:41

453

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generalization of positive-definite matrices to matrices over finite fields

Published on 26 Mar 2026 - 12:40

957

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Is it possible to define the tensor product of two vectors with respect to a bilinear form?

Published on 26 Mar 2026 - 12:37

305

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Canonical bundle of the Lagrangian Grassmannian

Published on 25 Mar 2026 - 15:41

116

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How to show using the universal property that $V\otimes V^{\ast} \cong \mathcal{L}(V,V)$?

Published on 26 Mar 2026 - 6:21

List Question

"Quadratic" form between a 4th order tensor and a matrix

The natural map $V^* \times W \to \text{Hom}(V,W) $ Is bilinear.

$C(S \times T)$ is isomorphic to $C(S) \otimes C(T).$

Linear Algebra books that also covers multilinear algebra

Determinant function theorem

Prove that $\text{tr} (\phi \otimes \psi) = \text {tr} \phi \text {tr} \psi $.

$x_{\alpha}\in E$ and $y_{\beta} \in F$ are linearly independent then so are the vectors $\varphi(x_{\alpha},y_{\beta})$ iff $\otimes_2$ holds

Rank of 3-fold tensor in terms of matrix unfoldings proof

Is every abstract vector a tensor?

Is notational compactness in tensors (compared to linear algebra) relevant?

Exterior algebra of a ring

generalization of positive-definite matrices to matrices over finite fields

Is it possible to define the tensor product of two vectors with respect to a bilinear form?

Canonical bundle of the Lagrangian Grassmannian

How to show using the universal property that $V\otimes V^{\ast} \cong \mathcal{L}(V,V)$?

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