Question

Antisymmetry of exterior product for alternating multilinear forms

score 213 · Answer 1 · 2017-10-24 20:46:34

213

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Antisymmetry of exterior product for alternating multilinear forms

Published on 24 Oct 2017 - 20:46

score 145 · Answer 2 · 2017-10-27 00:08:36

145

Views

$\phi:\mathbb{R}^m\times \mathbb{R}^m\to\mathbb{R}$ alternating form of deg $2$. If $m$ is odd, $\exists v\neq 0$, $\phi(v,w) = 0$

Published on 27 Oct 2017 - 0:08

score 984 · Answer 3 · 2017-10-27 07:13:47

984

Views

Wedge product of vectors and of linear functionals

Published on 27 Oct 2017 - 7:13

score 370 · Answer 4 · 2026-03-26 21:35:16

370

Views

Uniqueness in structure theorem for f.g. module over Dedekind domain

Published on 26 Mar 2026 - 21:35

score 931 · Answer 5 · 2017-10-31 03:01:13

931

Views

Wedge products, dual basis and exterior algebra in my real analysis book

Published on 31 Oct 2017 - 3:01

score 109 · Answer 6 · 2017-10-31 03:44:03

109

Views

Why is $f(x,y,z) dx \wedge dy + g(x,y,z) dx \wedge dz + h(x,y,z) dy\wedge dz$ a $2$-form?

Published on 31 Oct 2017 - 3:44

score 119 · Answer 7 · 2017-10-31 04:32:55

119

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$\lambda^*w = f\ dx$, $f:[a,b]\to\mathbb{R}$ continuous, $\lambda$ path, show $\int_{\lambda}$ is $\int_a^b f(x)\ dx$.

Published on 31 Oct 2017 - 4:32

score 86 · Answer 8 · 2017-10-31 20:32:27

86

Views

Condition for the $1$-form $f\omega$, being $f \in C(\Omega)$ and $\omega = \omega_1\text{d}x_1 + \omega_2\text{d}x_2$, to be closed.

Published on 31 Oct 2017 - 20:32

score 177 · Answer 9 · 2017-11-01 02:11:52

177

Views

Understanding my book's comments on a proof of Poincare's lemma

Published on 01 Nov 2017 - 2:11

score 3.2k · Answer 10 · 2026-03-27 07:49:44

3.2k

Views

Proving Wikipedia's formula on interior product of commutator of vector fields

Published on 27 Mar 2026 - 7:49

score 39 · Answer 11 · 2017-11-07 20:37:59

39

Views

If $\bigwedge^n V=0$, what can we say about the dimension of the vector space $V$ over an algebraically closed field $\mathbb{k}$?

Published on 07 Nov 2017 - 20:37

score 144 · Answer 12 · 2017-11-08 01:11:20

144

Views

Wedge product of regular $r$-forms

Published on 08 Nov 2017 - 1:11

score 127 · Answer 13 · 2017-11-10 08:06:47

127

Views

Matrix form of trivector triple product

Published on 10 Nov 2017 - 8:06

score 360 · Answer 14 · 2026-03-27 17:51:58

360

Views

Lie derivative in geometric algebra/Clifford algebra

Published on 27 Mar 2026 - 17:51

score 46 · Answer 15 · 2017-11-11 00:53:19

46

Views

Reducibility of the representation $\bigwedge^2(\mathbb{C}^4)$ of $U(4)$.

Published on 11 Nov 2017 - 0:53

List Question

Antisymmetry of exterior product for alternating multilinear forms

$\phi:\mathbb{R}^m\times \mathbb{R}^m\to\mathbb{R}$ alternating form of deg $2$. If $m$ is odd, $\exists v\neq 0$, $\phi(v,w) = 0$

Wedge product of vectors and of linear functionals

Uniqueness in structure theorem for f.g. module over Dedekind domain

Wedge products, dual basis and exterior algebra in my real analysis book

Why is $f(x,y,z) dx \wedge dy + g(x,y,z) dx \wedge dz + h(x,y,z) dy\wedge dz$ a $2$-form?

$\lambda^*w = f\ dx$, $f:[a,b]\to\mathbb{R}$ continuous, $\lambda$ path, show $\int_{\lambda}$ is $\int_a^b f(x)\ dx$.

Condition for the $1$-form $f\omega$, being $f \in C(\Omega)$ and $\omega = \omega_1\text{d}x_1 + \omega_2\text{d}x_2$, to be closed.

Understanding my book's comments on a proof of Poincare's lemma

Proving Wikipedia's formula on interior product of commutator of vector fields

If $\bigwedge^n V=0$, what can we say about the dimension of the vector space $V$ over an algebraically closed field $\mathbb{k}$?

Wedge product of regular $r$-forms

Matrix form of trivector triple product

Lie derivative in geometric algebra/Clifford algebra

Reducibility of the representation $\bigwedge^2(\mathbb{C}^4)$ of $U(4)$.

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