List questions from exterior-algebra

Published on 26 Mar 2021 - 18:27

130

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Show $φ^n= 0$ for $φ:V→V$ a linear endomorphism such that $\mathrm{tr}(\wedge^qφ) = 0$ and $\dim(V) = n$ a vector space.

Published on 28 Mar 2026 - 1:48

24

Views

To define a right $\mathbb H$-module on the exterior product $\Lambda^2 (\mathbb H^n)$

Published on 28 Mar 2021 - 14:39

167

Views

Generalizing the geometric interpretation of dot product to simple $k$-vectors

Published on 26 Mar 2026 - 17:35

247

Views

$\Omega^*(M)$ as a graded algebra over the ring of smooth functions. Is there a notion of basis?

Published on 25 Mar 2026 - 12:41

34

Views

Express a 3-form as a 2-form through a change of coordinates

Published on 13 Apr 2021 - 12:37

152

Views

Pseudoscalar and imaginary unit for a 4D space

Published on 26 Mar 2026 - 11:16

880

Views

General rule of a $k-$form wedge product with itself over the real numbers

Published on 19 Apr 2021 - 11:28

57

Views

Equivalence of definitons of the pfaffian (via permutations and exterior algebra)

Published on 22 Feb 2026 - 23:12

131

Views

Well-definedness of Wedge Product

Published on 22 Apr 2021 - 7:01

82

Views

Clifford map is injective for $B=0$.

Published on 28 Mar 2026 - 2:22

410

Views

Tensors that are not pure tensors

Published on 26 Apr 2021 - 21:34

214

Views

Determinant of matrix on wedge product of vector spaces

Published on 28 Apr 2021 - 19:49

185

Views

Tensor product of complexification

Published on 26 Mar 2026 - 1:00

109

Views

$\phi_1∧ ... ∧\phi_n = (det A) dx_1 ∧ ... dx_n$

Published on 02 May 2021 - 12:20

List Question

Wedge product linearly independent question

Show $φ^n= 0$ for $φ:V→V$ a linear endomorphism such that $\mathrm{tr}(\wedge^qφ) = 0$ and $\dim(V) = n$ a vector space.

To define a right $\mathbb H$-module on the exterior product $\Lambda^2 (\mathbb H^n)$

Generalizing the geometric interpretation of dot product to simple $k$-vectors

$\Omega^*(M)$ as a graded algebra over the ring of smooth functions. Is there a notion of basis?

Express a 3-form as a 2-form through a change of coordinates

Pseudoscalar and imaginary unit for a 4D space

General rule of a $k-$form wedge product with itself over the real numbers

Equivalence of definitons of the pfaffian (via permutations and exterior algebra)

Well-definedness of Wedge Product

Clifford map is injective for $B=0$.

Tensors that are not pure tensors

Determinant of matrix on wedge product of vector spaces

Tensor product of complexification

$\phi_1∧ ... ∧\phi_n = (det A) dx_1 ∧ ... dx_n$

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