# Questions tagged [tensor-decomposition]

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### What is the maximum of $\operatorname{Tr}(EUAU^\dagger)$ when $U$ is unitary?

Given matrices $E$ and $A$, is there a good way to obtain the maximizing unitary $U$ for the objective function $\operatorname{Tr}(EUAU^*)$? (I know that the maximizer of $\operatorname{Tr}(EU)$ is ...
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### Special case of CP decomposition

I am reading this article by Kolda. On page 21, it says: ...CP [decomposition] can be viewed as a special case of Tucker [decomposition] where the core tensor is superdiagonal and $P = Q = R$... ...
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### An svd-like tensor decomposition splitting a tensor into two lower-dimensional tensors and a singular vector

I have also posted this question on mathoverflow, but it seems there are a lot of questions related to SVDs here and a tag "tensor-decomposition", so I will give it a shot. I am looking for ...
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### The optimal solution of tensor Tucker decomposition problem

I have a question about tensor Tucker deocomposition. Recall that in Higher-Order Singular Value Decomposition (HOSVD), each factor matrices $U_i$ is obtained by taking the top $R_i$ left singular ...
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### How to build 2nd rank tensors from set of vectors?

Suppose we have 3 vectors: $A_i$, $B_i$, $C_i$, where $i=1,2,3$. How to build all possible dependent 2nd rank tensors based on these vectors? I believe, that at first we need to obtain all possible ...
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### Choosing an Irreducible Tensor Operator Basis where the Singular Values of Each Basis Element are the Same

Let $\mathcal{B(H)}$ be the space of all bounded linear operators on the Hilbert space $\mathcal{H}$. Let $g \rightarrow \mathcal{U}_g$, where $\mathcal{U}_g (\cdot):= U(g) (\cdot) U(g)^\dagger$, be ...
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### Integrating unitary vector in calculating stress resultant

The problem defines: velocity in the local base $\{e_r , e_\theta , e_z\}$, the gradient and acceleration in the local curvilignear base $e_{i} \otimes e_{j}$ avec $i, j \in\{r, \theta, z\}$ ...
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### Proof of 3-fold Tensor Uniqueness

In the notes linked below Professor Roughgarden states Theorem 3.1 without proof. http://timroughgarden.org/s17/l/l10.pdf Any ideas how one would go about proving this statement or references to ...
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### Tensor product raised to power $N$.

Can the following quantity be reduced to further $[A \otimes B + (\mathbb{1} - A) \otimes D]^N$, for positive interger $N$? Here, $\otimes$ denotes the Kronecker (tensor) product and the matrices $A$ ...
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### What are the matricization and vectorization of tensor products?

I'm trying to understand the concepts of matricization (matrix unfolding) and vectorization of tensor products. In the past, I've only dealt with tensor products of infinite-dimensional Banach and ...
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### If a tensor's multilinear rank is $(R,R,R)$, then is its canonical/CP rank also $R$?

Given an order $2$ tensor (i.e. a matrix), one always has that row rank is equal to the column rank, so that its multilinear rank or $n$-ranks is always equal to $(R,R)$ for some $R$. Moreover that $R$...
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### Readings on Tensors, Tensor Algebra and Tensor Decomposition

I have just started my Masters Degree in Mathematics and I will be focussing on Tensors (Viewed as Multidimensional Arrays) and Tensor decompositions. My professor is by no means an expert on Tensors ...