All Questions
8 questions
1
vote
0
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155
views
Some kind of product of two 2d tensors to create a 3d tensor?
I recently need to apply the following concept of product of two 2d tensors to create a 3d tensor (tensors understood as generalized arrays):
given two 2d tensors $A_{m\times n}$ and $B_{n\times p}$, ...
- 461
2
votes
2
answers
584
views
Can the eigenvalues of a real symmetric tensor be complex?
Let $T$ be a fully symmetric tensor of rank $3$ and size $N$.
Using the following definition of eigenvalues, let $x\in \mathbb{C}^N$ and $\lambda\in\mathbb{C}$ such that:
\begin{equation}
\sum_{jk}^...
- 117
3
votes
0
answers
262
views
Why some operations on tensors don't give a tensor? [closed]
I asked the following question on math.stackexchange but no one seemed to have an authorative answer so I'm posting here hoping that experts will see it.
The gradient is a tensor $\nabla f:\mathbf{V} \...
- 139
4
votes
1
answer
494
views
Characterization of all-orthogonal tensors
In the paper [1], it is proven in Theorem 2 that any $n$-tensor $\mathcal{A}\in\mathbb{R}^{d_1\times...\times d_n}$ can be decomposed as
$$
\mathcal{A}=\mathcal{S} \times_1 U_1 ...\times_n U_n
$$
...
- 41
2
votes
0
answers
77
views
Rank-1 decomposability of symmetric tensors
My question is about rank-1 decomposability of symmetric tensors over the reals.
Let $v_1,\dots,v_n\in\mathbb{R}^d$ be vectors. Construct the object:
$$
V=\sum_{j=1}^n \underbrace{v_j\otimes v_j\...
- 1,096
1
vote
0
answers
50
views
On symmetric tensors with same rank, different orders
Let $A,B$ be two symmetric tensors of same rank $m$; and orders $k$ and $\ell$, respectively. In particular, assume that $A,B$ admits the following structure: There exists $v_1,\dots,v_m\in\mathbb{R}^...
- 1,096
7
votes
1
answer
356
views
Is there any sort of higher-order SVD (quadratic and above) for dimensionality reduction?
(Posted this on math.stackexchange and cross.correlated over more than a week ago, but didn't get an answer, and this is a question in my research so this seems like it might have been the better ...
- 141
5
votes
1
answer
5k
views
Is there a generalization of eigenvalues and eigenvectors to tensors?
Two perhaps ill-posed or just silly questions:
Let $n>0$, $T$ be an $(n+2)$-tensor, and $\otimes$ denote the Kronecker product of tensors. Is there a tensor generalization for the fundamental ...
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