Suppose we have some tensor product of vector spaces. By tensor rank, I mean the minimal number of simple tensors required to write down an element of this tensor product of spaces. Is there much known about maps that preserve this tensor rank? Also an easier (more specific) question: suppose I’m working in $U(4)$. Might […]

This is a generalization of the currently unanswered question here. Let $k$ be a field, $A$ be a finite-dimensional $k$-algebra, and $M$, $N$ right and left $A$-modules, respectively, both finite dimensional over $k$. How can one compute the dimension (over $k$) of the tensor product $M\otimes_A N$? Let’s say $A$ has dimension $a$, $M$ has […]

Wikipedia says that a linear transformation is a $(1,1)$ tensor. Is this restricting it to transformations from $V$ to $V$ or is a transformation from $V$ to $W$ also a $(1,1)$ tensor? (where $V$ and $W$ are both vector spaces). I think it must be the first case since it also states that a linear […]

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