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Diagonalizability, orthogonal diagonalizability of higher order tensors and their being or not being dense in some suitable topology

For our discussion, we'll assume that we're working with $\mathbb{R}^m$ only, but much or all of the following discussion should be carried over immediately to any finite dimensional inner product ...
19 votes
2 answers
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Exponentiation of vector spaces?

This question occurred to me while thinking on another one here, Name for an operation on matrices? Can one define in an invariant way a binary operation on finite-dimensional vector spaces - let us ...