[dkarrasch]

Closes #184, closes #183.

LinearAlgebra.jl now provides generic lmul!/rmul! for HessenbergQ (JuliaLang/LinearAlgebra.jl#1704), with the same signatures as the methods defined in src/svd.jl. Redefining them overwrites the upstream methods, which is an error during precompilation, so GenericLinearAlgebra no longer precompiles against LinearAlgebra master (see JuliaLang/LinearAlgebra.jl#1782).

• Define the local HessenbergQ kernels only when LinearAlgebra lacks them, gated on hasmethod(lmul!, Tuple{LinearAlgebra.HessenbergQ,AbstractVecOrMat}). The upstream kernels handle the same element types, honour uplo, and are 13-29% faster on BigFloat in my measurements.
• The HessenbergQs built in BidiagonalFactorization.getproperty store their reflectors below the subdiagonal, which is the 'L' layout that hessenberg produces; mark them as such instead of 'U'. Also pass the matching τ type parameter for leftQ.
• Extend the HessenbergQ test to both factors, both bidiagonal orientations, real and complex BigFloat, all four multiplication directions, and the reconstruction of the original matrix.

Tested locally against LinearAlgebra master (upstream methods used) and on Julia 1.9.4 (local fallbacks used); the new testset passes in both configurations.

🤖 Generated with Claude Code

https://claude.ai/code/session_01Vv9VYe4nM23v8ruYwk9AQx

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Generated by Claude Code

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 95.79%. Comparing base (658cf62) to head (1212d7b).

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #185      +/-   ##
==========================================
+ Coverage   95.73%   95.79%   +0.06%     
==========================================
  Files          11       11              
  Lines        1524     1546      +22     
==========================================
+ Hits         1459     1481      +22     
  Misses         65       65              

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[IanButterworth]

Claude:

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Since 2026-10-12, GenericLinearAlgebra fails to precompile on Julia nightly (1.15-DEV): its lmul!(::HessenbergQ, ...) overwrites the LinearAlgebra method added in JuliaLang/LinearAlgebra.jl#1704 (stdlib bump JuliaLang/julia#63743). On PkgEval this also breaks its dependents, including DoubleFloats, CSVFiles and FileIO. The wrong-results concern in #183 was fixed by JuliaLang/LinearAlgebra.jl#1783, which julia master now includes. Could this be merged and released?

Written with Claude Code (Opus 5.5).

[dkarrasch]

Ideally, we would need an approving review by someone with write access. I have now included a version bump, and once tests pass I'll merge, bypassing the rules, given @araujoms approving review.

[dkarrasch]

Thanks, @andreasnoack!