# Questions tagged [tensor-decomposition]

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8 questions
1answer
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### Decomposition of the tensor product $\mathbb{Q}_p \otimes_{\mathbb{Q}} \mathbb{Q}[i]$ into a product of fields

I am trying to solve the following problem: For each rational prime $p$, describe the decomposition of the tensor product $\mathbb{Q}_p \otimes_{\mathbb{Q}} \mathbb{Q}[i]$ into a product of fields, ...
0answers
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### Does every subspace of the exterior algebra of dimension $>1$ contain a decomposable element?

Let $V$ be a real $n$-dimensional vector space, and let $W \le \bigwedge^k V$ be a subspace . Suppose that $\dim W \ge 2$. Does $W$ contain a non-zero decomposable element? If $\dim W=1$, then ...
1answer
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### Comparing the representation $T \otimes T$ in terms of matrices and $T^2$

Interpret the representation $T \otimes T$ in terms of matrices, and compare it with $T^2$. Could anyone give me a hint on how to solve this please ? EDIT: enter image description here enter ...
1answer
22 views

### Is “being decomposable” preserved under taking a subspace?

Let $V$ be a vector space over some field, and $W \le V$ a vector subspace. Let $1<k<\dim V$ be an integer. Suppose $\omega \in \bigwedge^k W$ is decomposable as an element in $\bigwedge^k V$....