# What is the point of the Symmetric type?

**URL:** <https://discourse.julialang.org/t/what-is-the-point-of-the-symmetric-type/40773>\
**Category:** Internals & Design\
**Tags:** linearalgebra\
**Created:** [June 4, 2020, 11:21pm UTC](https://discourse.julialang.org/t/what-is-the-point-of-the-symmetric-type/40773 "2020-06-04T23:21:17Z")\
**Posts on this page:** 1\
**Showing post:** 5

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**Author:** ![stevengj](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/stevengj/32/71_2.png) [@stevengj](https://discourse.julialang.org/u/stevengj)\
**Post date:** [June 5, 2020, 1:47am UTC](https://discourse.julialang.org/t/what-is-the-point-of-the-symmetric-type/40773/5 "2020-06-05T01:47:48Z")

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> [@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](http://icl.cs.utk.edu/lapack-forum/viewtopic.php?f=2&t=3592#p9189). 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.

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