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Questions about the properties of vector spaces and linear transformations, including linear systems in general.

30 votes
12 answers
14k views

Why are tensors a generalization of scalars, vectors, and matrices?

Take two vector spaces $V$ and $W$ over a field $F$. One may form the tensor product $V\otimes W$ and it fulfills an universal property. Elements of $V\otimes W$ are called tensors and they are linear …