What is the point of the Symmetric type?

[stevengj]

@Grayscale

Do you know why then there is a SymTridiagonal type but no HermTridiagonal ?

I tend to agree that we should have HermTridiagonal instead, but you should realize that any Hermitian tridiagonal matrix T can be converted to a similar real-symmetric tridiagonal matrix T' = D^* T D by a unitary diagonal scaling matrix D — see e.g. the discussion here. So, in principle, you can always work with real tridiagonal matrices.

For the same reason LAPACK’s eigensolver for complex Hermitian matrices first reduce them to similar real-symmetric tridiagonal matrices (this is done by the hessenberg factorization routine in Julia), and it was to reflect these routines that SymTridiagonal was first introduced.

@Oscar_Smith

I’d argue that Symmetric is important for the significant portion of people who use LinearAlgebra but don’t do anything with complex numbers or have a significant Mathy background.

Those people can just use Hermitian too. For real matrices, Hermitian and Symmetric are equivalent. Even if they don’t know the word “Hermitian,” learning a new word is not such a big obstacle.