Symbolic diagonalization

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Dear community,

I was wondering to what extend diagonalization in Symbolics.jl is implemented,

Symbolic linear algebra (factorizations, inversion, determinants, eigencomputations, etc.)

I see that some factorizations are working, but what about diagonalization of a normal matrix?

Best,

v.

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Won’t that be equivalent to solving the characteristic polynomials and so it won’t be possible for n>5 by Abel’s Theorem to do symbolically? I haven’t thought about it too much but @YingboMa might have an idea.

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See symbolic diagonalization of a matrix - MathOverflow for a discussion of the general case. Maybe something more specific can be said about normal matrices. With symbolic matrices, I guess one needs to add some constraints on the terms in order to guarantee that they are normal.

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Agree, but even for n<5 that diagonalization can prove to be useful. On the other hand, there are some special matrices which can be solved also exactly, I guess one needs to keep a little database of those guys somewhere.