this post was submitted on 03 Oct 2024
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Sometimes, you can reorient your problem such that a matrix or tensor has only diagonal entries, making it easier to handle.
For example by choosing new unit vectors or by changing the set of functions describing the problem (whatever is the thing that the matrix or tensor is tied to).
Only diagonal entries in a matrix is basically just n simple functions with no crossover, right?
Key advantage of a diagonal matrix is that all off-diagonal entries are zero, so yes, no crossover of functions (or basis elements).
But the functions may be as ugly as they please and there may be an infinite number of them.