List questions from multilinear-algebra

Published on 24 Dec 2021 - 8:33

200

Views

The volume element determined by some inner product and orientation

Published on 25 Dec 2021 - 7:37

90

Views

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 31 Mar 2026 - 6:02

233

Views

Invariant polynomial function on Lie algebras.

Published on 27 Mar 2026 - 21:34

121

Views

Why in the union $\bigcup_{p \in U}T_p^(\mathbb{R}^n)$ all of the sets $T_p^(\mathbb{R}^n)$ are disjoint?

Published on 07 Jan 2022 - 10:33

99

Views

Northcott Multilinear Algebra Universal Property Proof

Published on 27 Mar 2026 - 14:58

135

Views

Solution to a linear equation involving a skew-symmetric tensor

Published on 26 Mar 2026 - 23:09

48

Views

A $3\times3$ matrix is multiplied by an unknown $3\times1$ matrix and if the result is $\mathbf{0}$ how do I compute the unknown matrix?

Published on 10 Jan 2022 - 20:22

164

Views

Generalization of "symmetric positive definite" to higher dimensions?

Published on 13 Jan 2022 - 22:28

109

Views

Matrix-rank nonincreasing unitary tensor operations

Published on 23 Feb 2026 - 10:43

160

Views

Do all bilinear forms have a signature?

Published on 30 Mar 2026 - 16:48

102

Views

What allows a bilinear form (output: field element) to also work as a linear map (output: vector)?

Published on 30 Mar 2026 - 16:49

310

Views

Calculating simple pullbacks

Published on 03 Mar 2022 - 17:30

545

Views

Proof that pullback commutes with exterior derivative

Published on 04 Mar 2022 - 4:55

1.1k

Views

What is a top form?

Published on 11 Mar 2022 - 2:01

List Question

Why does $\det A$ change sign when any $2$ columns of $A$ are interchanged?

The volume element determined by some inner product and orientation

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

Invariant polynomial function on Lie algebras.

Why in the union $\bigcup_{p \in U}T_p^(\mathbb{R}^n)$ all of the sets $T_p^(\mathbb{R}^n)$ are disjoint?

Northcott Multilinear Algebra Universal Property Proof

Solution to a linear equation involving a skew-symmetric tensor

A $3\times3$ matrix is multiplied by an unknown $3\times1$ matrix and if the result is $\mathbf{0}$ how do I compute the unknown matrix?

Generalization of "symmetric positive definite" to higher dimensions?

Matrix-rank nonincreasing unitary tensor operations

Do all bilinear forms have a signature?

What allows a bilinear form (output: field element) to also work as a linear map (output: vector)?

Calculating simple pullbacks

Proof that pullback commutes with exterior derivative

What is a top form?

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