Questions tagged [tensor]
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14 questions from the last 365 days
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Invariant theory for unitary groups $\mathcal{U}(n)$
I'm trying to understand the invariant theory of the unitary groups $\mathcal{U}(n)$ on tensor powers of its standard representation $V^{\otimes p} \otimes (V^*)^{\otimes q}$. Let $\mathcal{U}(n)$ ...
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Question on Lorentzian geometry
I apologize in advance if this is a too basic question.
Let $(M,g)$ be a Lorentzian manifold with signature convention $(-,+,\dots,+)$. Now, lets suppose $X\in\Gamma(TM)$ defines a global time-...
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Can the derivative of eigenvectors with respect to its components be taken as zero if all eigenvalues are equal?
I want to ask a couple of follow up questions to the question answered on the thread "Derivative of eigenvectors of a matrix with respect to its components".
I noticed that in the accepted ...
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Space of all orthogonal partially complex $2\times2\times2$ tensors
I am trying to understand the space of all orthogonal tensors, I asked a more general version of this question here but with no solution yet found. I want to look at the simplest case first, namely a $...
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Space of all orthogonal $2\times2\times2$ tensors
I am trying to understand the space of all orthogonal tensors, a question asked here before but with no real solution yet found. The solutions for order-$2$ tensors are clear so thus the simplest case ...
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Adjoint to "strict twocategory of strict twofunctors"
Let C be the category of strict twofunctors, featuring the addition of a Grothendieck universe. Strict twocategories are categories enriched over the category of categories.
C has an internal hom ...
user531303
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Can numerical differentiation be applied to tensor derivatives?
I know that for a 1D function, I can calculate the numerical derivative at every point, $\DeclareMathOperator{\d}{d\!} (x_1,y_1)$, with $\d y/\d x$ where $\d y = y_2 - y_0$ and $\d x = x_2 - x_0$. If ...
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Combination of simple tensors - II
This is a follow-up question to Combination of simple tensors.
I am interested in devising an alternative norm (I mean, other than the usual $\pi$ or $\epsilon$ norms) in the tensor product of two ...
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Combination of simple tensors
I aksed this question on Math Stack Exchange 6 days ago, with no answer: https://math.stackexchange.com/q/4875445/1297919
Let $X$ and $Y$ two Banach spaces and let $X\otimes Y$ their tensor product. ...
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Bochner Laplacian in coordinates
Sorry if this is a too basic question, but I didn't find an answer anywhere:
The connection Laplacian, or Bochner Laplacian, is the differential operator acting on $k$-tensor fields $T\in\Gamma^{\...
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Is the asymptotic rank of a tensor bounded by (naive) border rank?
Write $R(T)$ for the rank of an order-$3$ tensor $T \in \mathbb C^{m \times n \times p}$ over the complex numbers. If $T' \in \mathbb {C}^{m' \times n' \times p'}$ is another such tensor then let $T \...
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What is the best known bound for the bilinear complexity of $4\times 4$ matrices product
Assume we work on the complex field $\mathbb{C}$. And we use $\langle p,q,r\rangle$ to denote the bilinear complexity of product of a $p\times q$ matrix and a $q\times r$. Recently I read a paper on ...
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What is expected (border) rank of the knonecker product of 3-tensors
Given two three order tensors $T$ and $S$ in $F^{m\times n\times p}$ and $F^{a\times b\times c}$. Clearly $\operatorname{rk}(T\otimes S)\le \operatorname{rk}(T)\operatorname{rk}(S)$. Does the equality ...
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How far is the slice rank of a tensor from its CP rank
Assume we work on any infinite field and 3-ordered tensor. Clearly for any tensor $T$, we have $\operatorname{srk}(T)\le \operatorname{rk}(T)$. Here, $\operatorname{srk}(T)$ (resp. $\operatorname{rk}(...
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