# Solving linear system BC = X where B is a symmetric positive semi-definite matrix

**URL:** <https://discourse.julialang.org/t/solving-linear-system-bc-x-where-b-is-a-symmetric-positive-semi-definite-matrix/115280>\
**Category:** Performance\
**Tags:** linearalgebra, matrices, linearsolve\
**Created:** [June 6, 2024, 12:52pm UTC](https://discourse.julialang.org/t/solving-linear-system-bc-x-where-b-is-a-symmetric-positive-semi-definite-matrix/115280 "2024-06-06T12:52:10Z")\
**Posts on this page:** 1\
**Showing post:** 7

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**Author:** ![gdalle](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/gdalle/32/27854_2.png) [@gdalle](https://discourse.julialang.org/u/gdalle)\
**Post date:** [June 6, 2024, 3:06pm UTC](https://discourse.julialang.org/t/solving-linear-system-bc-x-where-b-is-a-symmetric-positive-semi-definite-matrix/115280/7 "2024-06-06T15:06:41Z")

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Have you considerd using StaticArrays.jl, perhaps in conjunction with the custom BLAS methods mentioned here?

> [@Package to avoid allocations in some functions when using StaticArrays.jl](https://discourse.julialang.org/t/package-to-avoid-allocations-in-some-functions-when-using-staticarrays-jl/114539):
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> Hi! As I mentioned before, I am trying to build a full satellite attitude control subsystem (ACS) using Julia, which maybe one day will hopefully fly in a CubeSat. One very important requirement is to avoid runtime allocations. The entire system is built using StaticArrays from StaticArrays.jl and I manage to create a mockup of an entire ACS without allocations except for one single case: the Kalman filters. We need to use at least two Kalman filters in our project: one for the attitude and o…

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