# JuMP: Hermitian matrix variable and complex numbers in model

**URL:** <https://discourse.julialang.org/t/jump-hermitian-matrix-variable-and-complex-numbers-in-model/34230>\
**Category:** Optimization (Mathematical)\
**Tags:** question, complex-numbers\
**Created:** [February 5, 2020, 11:26pm UTC](https://discourse.julialang.org/t/jump-hermitian-matrix-variable-and-complex-numbers-in-model/34230 "2020-02-05T23:26:24Z")\
**Posts on this page:** 1\
**Showing post:** 2

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**Author:** ![ccoffrin](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/ccoffrin/32/400_2.png) [@ccoffrin](https://discourse.julialang.org/u/ccoffrin)\
**Post date:** [February 6, 2020, 12:24am UTC](https://discourse.julialang.org/t/jump-hermitian-matrix-variable-and-complex-numbers-in-model/34230/2 "2020-02-06T00:24:40Z")

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This is the place in PowerModels where the basic SDP relaxation constraint is added,

> <https://github.com/lanl-ansi/PowerModels.jl/blob/34fc00242deebf20c6f7eba45969f3a9d64f187a/src/form/wrm.jl#L25>

For a complex matrix W the encoding is, [\Re(W), \Im(W); -\Im(W), \Re(W)] \succeq 0. The Mosek manual is a fantastic refrence for SDP modeling tricks like this.

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