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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