# Questions tagged [tensor-decomposition]

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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 ...
1 vote
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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 ...
215 views

### Schouten theorem and doubts in the calculation of the tensor derivative

I am working on the following theorem Theorem (J. A. Schouten) For $n\geq 4$ the metric $g$ is conformally flat if and only if $W=0$. For $n=3$, the metric $g$ is conformally flat if and only if the ...
1 vote
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### References to Q-curvature

I am working on Q-curvature: $$Q^n_g= \frac{1}{2(n-1)} \Delta_g R_g+\frac{n^3-4n^2+16n-16}{8(n-1)^2(n-2)^2}\:R_g-\frac{2}{(n-2)^2}\:| Ric |^2_g$$ See, for example, the expression (3) in https://...
1 vote
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### SVD in scipy and numpy for tensors

Can someone explain to me the difference between SVD of numpy and scipy for Multidimensional arrays (Tensors)? ...
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### A tensor over $\mathbb R$ is sum of two decomposable tensors

Let $W$ be a vector space over $\mathbb R$ with basis $\{a,b\}$. Consider the tensor $$a \otimes a \otimes a - b \otimes b \otimes a + a \otimes b \otimes b + b \otimes a \otimes b.$$ a) Show that ...
1 vote
48 views

### Tensor Notation ambiguity

Sorry for this silly question, but this notation keeps popping up in my face in too many different places without any clarification, so I will be so grateful if someone can help and answer my question:...
1 vote
117 views

### Frobenius norm optimization problem

How to solve the following optimization problem which arises in the field of Higher Order SVD? Let $A \in \mathbb{R}^{m\times n}$, $W \in \mathbb{R}^{m\times l}$. find $\arg \max _{A}\|A^T W\|_F$ s.t. ...
70 views