List questions from multilinear-algebra

Published on 24 Jun 2013 - 21:28

431

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Prove that $\phi_1 \wedge \cdots \wedge \phi_k (v_1, \cdots, v_k) = \frac{1}{k!}\det[\phi_i(v_j)].$

Published on 29 Mar 2026 - 6:07

6.8k

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efficient summation of $\sum_{i=1}^{n}\sum_{j=1}^{n}\sum_{k=1}^{n}\sum_{l=1}^{n}A_{ij}A_{ik}A_{il}A_{jk}A_{jl}A_{kl}$

Published on 27 Jun 2013 - 1:16

7k

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A user's guide to Penrose graphical notation?

Published on 01 Jul 2013 - 13:39

162

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What is $(V^)^{\otimes l} \stackrel{f}{\rightarrow} S^l( (V^)^{\oplus l} )\cong S^l( (V^{\oplus l})^* ) \stackrel{g}{\rightarrow} S^l(V^*)$?

Published on 07 Jul 2013 - 8:47

237

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Computing distances between hyperspheres and sides of a hypercube?

Published on 16 Jul 2013 - 18:30

1.7k

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Quick question: tensor product and dual of vector space

Published on 19 Jul 2013 - 1:23

253

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Linear map induced by bilinear maps

Published on 23 Jul 2013 - 8:24

104

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Facts about the tensor product

Published on 24 Jul 2013 - 14:26

680

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Bilinear Form - Proof

Published on 26 Jul 2013 - 10:49

175

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bilinear form - proof

Published on 26 Jul 2013 - 10:29

42

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Help with substituting definitions into tensor

Published on 26 Jul 2013 - 18:01

1.6k

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Trace of the $n$-th symmetric power of a linear map

Published on 29 Jul 2013 - 4:10

40

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Terminology for multilinear functionals the sum of whose cyclic shifts is zero?

Published on 30 Jul 2013 - 17:41

292

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Universal property definition from Greub's Multilinear Algebra

Published on 02 Aug 2013 - 20:10

List Question

For covariant tensors, why is it $\bigwedge^k(V)$, not $\bigwedge^k(V^*)$?

Prove that $\phi_1 \wedge \cdots \wedge \phi_k (v_1, \cdots, v_k) = \frac{1}{k!}\det[\phi_i(v_j)].$

efficient summation of $\sum_{i=1}^{n}\sum_{j=1}^{n}\sum_{k=1}^{n}\sum_{l=1}^{n}A_{ij}A_{ik}A_{il}A_{jk}A_{jl}A_{kl}$

A user's guide to Penrose graphical notation?

What is $(V^)^{\otimes l} \stackrel{f}{\rightarrow} S^l( (V^)^{\oplus l} )\cong S^l( (V^{\oplus l})^* ) \stackrel{g}{\rightarrow} S^l(V^*)$?

Computing distances between hyperspheres and sides of a hypercube?

Quick question: tensor product and dual of vector space

Linear map induced by bilinear maps

Facts about the tensor product

Bilinear Form - Proof

bilinear form - proof

Help with substituting definitions into tensor

Trace of the $n$-th symmetric power of a linear map

Terminology for multilinear functionals the sum of whose cyclic shifts is zero?

Universal property definition from Greub's Multilinear Algebra

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