All Questions
Tagged with tensor multilinear-algebra
8 questions with no upvoted or accepted answers
4
votes
0
answers
126
views
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 ...
- 101
4
votes
0
answers
232
views
Pseudo-tensor- and tensor-densities: Sections of what bundle?
Let $\mathcal{M}$ be a smooth manifold. A tensor field is then usually defined to be a section of the tensor bundle
$$\bigotimes_{i=1}^{p}T\mathcal{M}\otimes\bigotimes_{i=1}^{q}T^{\ast}\mathcal{M}.$$
...
- 1,171
4
votes
0
answers
171
views
Cannot multivectors be classified more easily than general tensors?
This is sort of a spinoff of Is there a useful generalization of the Schmidt decomposition to the tensoring together of 3 or more vector spaces? - seems to be almost hopeless, but maybe some partial ...
- 18.4k
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
124
views
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 $...
- 101
1
vote
0
answers
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
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
0
votes
0
answers
55
views
Solving nonlinear differential multi-variable equation with block-matrices
Here is the problem:
Given a formula $f:\mathbb{R}^{n+k}\rightarrow\mathbb{R}^n$, written as $f(x_1(t),x_2(t),...,x_n(t);a1,...ak)$ with $k$ real unknown parameters $a_1,...,a_k$. For any $(a1,...ak)$,...
