# Tagged Questions

For questions about vector spaces and their properties. More general questions about linear algebra belong under the [tag:linear-algebra] tag. A vector space is a space which consists of elements called "vectors", which can be added and multiplied by scalars. In other words, these are the spaces ...

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### What's the difference between $V\times W$ and $V\otimes W$ where $V$ and $W$ are vector space?

Let $V,W$ vector spaces. I don't really understand what is $V\otimes W$. To me it looks the same that $V\times W$. Do you have any explanation ?
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### Set of orthogonal vectors in $\mathbb{R}^n$

How can we show that a set of pairwise orthogonal vectors in $\mathbb{R}^n$ has size at most $n$? I know it seems very intuitive, but not sure what the formal proof would look like (whether "...
If I have a vector space $V^{(1)}\otimes V^{(2)}$ and I have some ray $\sum\limits_k x_k s_k\otimes s'_k = s\otimes \sum\limits_k x_k s'_k$, is the only solution that $s_k = s$ $\forall$ $k$? All $x_k$...