[ViralBShah]

#1126 made sparse cond return Inf for a singular matrix, but its docstring does not say so, nor that rounding can hide the singularity. Raised in the post-merge review of #1126.

The material is the behaviour on main:

julia> cond(sparse([1.0 2; 3 6]), 1)
Inf

julia> A = [1.0 2 3; 4 5 6; 7 8 9];   # singular

julia> cond(sparse(A), 1), cond(A, 1)
(1.0808639105689187e17, Inf)

The UMFPACK LU of the second matrix ends with a pivot that rounding leaves nonzero, while LAPACK's partial pivoting meets an exact zero, so the docstring says that a finite but very large result can still mean a singular matrix, and that sparse and dense can disagree on which case they report.

Written by Claude Code.

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[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 94.70%. Comparing base (2bef1fd) to head (96793cd).

Additional details and impacted files

@@           Coverage Diff           @@
##             main    #1130   +/-   ##
=======================================
  Coverage   94.70%   94.70%           
=======================================
  Files          16       16           
  Lines       10423    10423           
=======================================
  Hits         9871     9871           
  Misses        552      552           

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