List questions from exterior-algebra

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Embedding from exterior product to tensor product space

Published on 14 Nov 2021 - 11:08

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Intuitive understanding of oriented volume and trivectors

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What is meant by the wedge product?

Published on 30 Nov 2021 - 12:32

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Every $(n-1)$-form is decomposable

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Hodge star and non-orthonormal basis

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Equivalence of definition of wedge product on $\mathrm{End}(E)$.

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Explicit isomorphism $\Lambda^2\Lambda^2V\oplus\Lambda^4V\cong V\otimes\Lambda^3V$

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Where does this permutation product live?

Published on 07 Dec 2021 - 16:28

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How do you show that $e_{I}^{}(e_{J}):=\delta_{I,J}$ is a basis for $(\Lambda_{k}V)^{}$, $\Lambda_{k}V:= V^{\otimes k}/A$?

Published on 09 Dec 2021 - 18:08

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Computing the wedge product of some differentials

Published on 12 Dec 2021 - 16:51

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substituting values in a wedge expression $\omega=zdx \wedge dy \in A^2(R^3)$ given function g

Published on 16 Dec 2021 - 8:01

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Prove that $\theta: M^m \rightarrow T^mM$ such that$ (x_1,...,x_m) \rightarrow \frac{1}{m!} \sum_{σ∈Sm}ε(σ)x_{σ(1)} ⊗ · · · ⊗ x_{σ(m)}$ is alternating

Published on 18 Dec 2021 - 17:16

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Different definitions on the tensor and wedge products

Published on 25 Dec 2021 - 13:55

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Show that $\big\{A(v_{i_1}\otimes \cdots\otimes v_{i_k})\in V^{\wedge k}:i_1<\cdots<i_k \big\} $ is linearly independent

Published on 30 Dec 2021 - 19:38

List Question

Decomposition of Hodge Operator

Embedding from exterior product to tensor product space

Intuitive understanding of oriented volume and trivectors

What is meant by the wedge product?

Every $(n-1)$-form is decomposable

Hodge star and non-orthonormal basis

Equivalence of definition of wedge product on $\mathrm{End}(E)$.

Explicit isomorphism $\Lambda^2\Lambda^2V\oplus\Lambda^4V\cong V\otimes\Lambda^3V$

Where does this permutation product live?

How do you show that $e_{I}^{}(e_{J}):=\delta_{I,J}$ is a basis for $(\Lambda_{k}V)^{}$, $\Lambda_{k}V:= V^{\otimes k}/A$?

Computing the wedge product of some differentials

substituting values in a wedge expression $\omega=zdx \wedge dy \in A^2(R^3)$ given function g

Prove that $\theta: M^m \rightarrow T^mM$ such that$ (x_1,...,x_m) \rightarrow \frac{1}{m!} \sum_{σ∈Sm}ε(σ)x_{σ(1)} ⊗ · · · ⊗ x_{σ(m)}$ is alternating

Different definitions on the tensor and wedge products

Show that $\big\{A(v_{i_1}\otimes \cdots\otimes v_{i_k})\in V^{\wedge k}:i_1<\cdots<i_k \big\} $ is linearly independent

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