I usually work with full diagonalisation of Hermitian matrices. After some research I realised that there are two options to retrieve the eigenvalues and eigenvectors of such a matrix.

`LinearAlgebra.LAPACK.syev!()`

and `eigen!()`

. From the source code of `eigen!()`

it seems that it is calling a general eigensolver routine called `ggevx()`

.

The `LinearAlgebra.LAPACK.syev!()`

routine required some digging into the source code to figure out that it is also intended for Hermitian matrices (docs.julialang.org only talks about symmetric matrices). I realised that it is calling specialised Hermitian routines in LAPACK.

Now after building up a 2000x2000 Hermitian matrix I called both routines the following way and timed their peformance:

```
H = weyl(10, 10, 10)
Ht = deepcopy(H)
@time eigsys = LAPACK.syev!('V', 'U', H)
@time eigsyst = eigen!(Hermitian(Ht))
```

To my surprise the `eigen!`

routine is quite a bit faster:

```
8.998029 seconds (6 allocations: 1.068 MiB)
6.128692 seconds (16 allocations: 123.658 MiB, 1.71% gc time)
```

To me this is quite counterintuitive behaviour. I would have guessed that the specialised routines should work faster.