[ViralBShah]

Stacked on #1131.

Since #1126 sparse cond wraps the whole opnormestinv estimator in a try, so a SingularException from anywhere inside it becomes Inf, and a singular triangular or diagonal matrix is only found once the estimator has allocated its blocks and run its first solve. Raised in the post-merge review of #1126.

Before (#1131), cond(A, 1) of a singular A with n = 10^6 and one zero on the diagonal

A	time	allocated
diagonal	64.6 ms	125.3 MiB
lower bidiagonal	16.1 ms	68.7 MiB

After

A	time	allocated
diagonal	9.4 ms	56.6 MiB
lower bidiagonal	2.6 ms	0

Both return Inf, before and after. factorize throws a SingularException for a singular LU, and for a singular Hermitian matrix once Cholesky and LDLt have failed and it falls back to the LU (#1116); only the triangular and diagonal factors it returns leave the zero pivot to the solve. So cond now catches around factorize alone and checks the diagonal of those factors with _issingularfactor, which reuses the triangular solve's _trisingular, before it calls the estimator; opnormestinv(A, t) keeps its behaviour and calls the new _opnormestinv(A, F, t) with the factorization. A sweep of cond against dense over Int, Float32, Float64, ComplexF32, ComplexF64, Rational{Int}, BigFloat and Complex{BigFloat}, on general, singular, triangular, diagonal and Hermitian matrices, gives the same results as #1131 with a seeded RNG.

Written by Claude Code.

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[codecov]

Codecov Report

❌ Patch coverage is 85.71429% with 2 lines in your changes missing coverage. Please review.
✅ Project coverage is 94.68%. Comparing base (82a0880) to head (ef013bb).

Files with missing lines	Patch %	Lines
src/linalg.jl	85.71%	2 Missing ⚠️

Additional details and impacted files

@@                   Coverage Diff                   @@
##           vs/cond-result-type    #1132      +/-   ##
=======================================================
- Coverage                94.70%   94.68%   -0.02%     
=======================================================
  Files                       16       16              
  Lines                    10424    10432       +8     
=======================================================
+ Hits                      9872     9878       +6     
- Misses                     552      554       +2     

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