List questions from multilinear-algebra

Published on 08 Oct 2019 - 4:06

273

Views

The endomorphisms of $\mathbb{R}^3$ form an abelian group?

Published on 16 Oct 2019 - 17:56

442

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Form of a 2-form if and only if wedge is zero.

Published on 28 Oct 2019 - 5:08

44

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Map sending $k$-linear functions in $V_1\times V_2\times\cdots \times V_n$ into linear maps in $V_1 \otimes V_2 \otimes \cdots\otimes V_n$

Published on 31 Oct 2019 - 20:31

612

Views

Wedge product of alternating forms is again alternating – Definition with shufles

Published on 04 Nov 2019 - 10:45

123

Views

Why is the derivative of a $m$-linear map the sum of $(m−1)$-linear functions

Published on 06 Nov 2019 - 9:29

174

Views

Prove that the derivative of a multilinear map is continuous

Published on 08 Nov 2019 - 0:43

29

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Prove that if $\partial^m f(a)$ exists then $\partial^m f(a) \in \mathcal L_\text{sym}^m (E,F)$

Published on 11 Nov 2019 - 19:21

77

Views

Compute $\partial_j (\partial^m f)(x)$ in terms of $\partial_{j_1} \partial_{j_2} \cdots \partial_{j_{m+1}} f(x)$

Published on 13 Nov 2019 - 2:20

468

Views

Hessian squared and Laplacian on a Riemannian manifold

Published on 25 Mar 2026 - 18:48

175

Views

Finite-dimensional associative algebra over an algebraically closed field

Published on 25 Mar 2026 - 7:41

45

Views

Set of anti-invariant forms over the $n$-sphere question

Published on 26 Dec 2019 - 20:52

196

Views

Constant velocity rotating helix position

Published on 08 Jan 2020 - 22:04

69

Views

Differential of a tensor field

Published on 10 Jan 2020 - 0:23

147

Views

Computing differential of a $0$-form

Published on 14 Jan 2020 - 14:08

List Question

How does the universal property ensure finitely many nonzero vectors?

The endomorphisms of $\mathbb{R}^3$ form an abelian group?

Form of a 2-form if and only if wedge is zero.

Map sending $k$-linear functions in $V_1\times V_2\times\cdots \times V_n$ into linear maps in $V_1 \otimes V_2 \otimes \cdots\otimes V_n$

Wedge product of alternating forms is again alternating – Definition with shufles

Why is the derivative of a $m$-linear map the sum of $(m−1)$-linear functions

Prove that the derivative of a multilinear map is continuous

Prove that if $\partial^m f(a)$ exists then $\partial^m f(a) \in \mathcal L_\text{sym}^m (E,F)$

Compute $\partial_j (\partial^m f)(x)$ in terms of $\partial_{j_1} \partial_{j_2} \cdots \partial_{j_{m+1}} f(x)$

Hessian squared and Laplacian on a Riemannian manifold

Finite-dimensional associative algebra over an algebraically closed field

Set of anti-invariant forms over the $n$-sphere question

Constant velocity rotating helix position

Differential of a tensor field

Computing differential of a $0$-form

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