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Generic numerical linear algebra in Julia

Results 32 GenericLinearAlgebra.jl issues
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Any chance of getting `sqrt` to work? It seems like LinearAlgebra makes assumptions about what schur returns in [this function](https://github.com/JuliaLang/julia/blob/8cbe1297f98aa477da5d98ebfaa4027205b35440/stdlib/LinearAlgebra/src/dense.jl#L884). Example: ```julia julia> using GenericLinearAlgebra s julia> A = rand(BigFloat,...

``` using GenericLinearAlgebra svd(big.([1,2;3,4])) ``` returns ``` UndefVarError: svd not defined Stacktrace: [1] top-level scope @ In[2]:1 [2] eval @ .\boot.jl:373 [inlined] [3] include_string(mapexpr::typeof(REPL.softscope), mod::Module, code::String, filename::String) @ Base .\loading.jl:1196...

This PR adds large matrix inversion. I feel it might fit here under the category of "A place to experiment with fast linear algebra routines written in Julia" It is...

From: https://github.com/JuliaLang/LinearAlgebra.jl/issues/203 @mschauer wrote: It would be nice to have a the semidefinite Cholesky or LDL' decomposition, which allows semidefinite matrices, is more stable and avoids computation of square roots....

Which the LinearAlgebra version has. ```julia julia> H = hessenberg(randn(3,3)) Hessenberg{Float64, UpperHessenberg{Float64, Matrix{Float64}}, Matrix{Float64}, Vector{Float64}, Bool} Q factor: 3×3 LinearAlgebra.HessenbergQ{Float64, Matrix{Float64}, Vector{Float64}, false}: 1.0 0.0 0.0 0.0 -0.783288 0.621658 0.0...

```julia using GenericLinearAlgebra A = zeros(BigFloat, 2, 2) F = GenericLinearAlgebra.svd(A, full = false) LinearAlgebra.SVD{BigFloat, BigFloat, Matrix{BigFloat}} U factor: 2×2 Matrix{BigFloat}: 0.0 0.0 0.0 0.0 singular values: 2-element Vector{BigFloat}: 0.0...

A small fix to make the generic ``eigen`` work for matrices that are hermitian by value but not by type, following @dlfivefifty's suggestion at https://discourse.julialang.org/t/eigen-not-working-for-arbitrary-precision-bigfloat/67686/11

Both in 1.6.2 and 1.7b3, see examples below with BigFloat. ```julia julia> versioninfo() Julia Version 1.6.2 Commit 1b93d53fc4 (2021-07-14 15:36 UTC) Platform Info: OS: macOS (x86_64-apple-darwin18.7.0) CPU: Intel(R) Core(TM) i7-8569U...

See https://github.com/JuliaLang/julia/pull/9804

The general type piracy in this package here, `GenericSVD` and `GenericSchur` recently broke precompile across an incredibly large number of packages, for example pretty much all of Queryverse. This PR...