feat(LinearAlgebra/Matrix): diagonal matrices with nonnegative entries are totally nonnegative

[sqrt-of-2]

---

This follow-up PR was suggested by @Vierkantor in #41813 (comment).

This contribution was created during "Formalizing Mathematics in Lean" held in Utrecht in August 2026.

[github-actions]

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[github-actions]

PR summary deca326651

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

---

Declarations diff (regex)

+ IsTotallyNonneg.diagonal
+ IsTotallyNonneg.diagonal_const

You can run this locally as follows

## from your `mathlib4` directory:
git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci

## summary with just the declaration names:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh <optional_commit>

## more verbose report:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh long <optional_commit>

The doc-module for scripts/pr_summary/declarations_diff.sh in the mathlib-ci repository contains some details about this script.

Declarations diff (Lean -- stale, waiting for the new build)

✅ Lean-aware diff — post-build, computed from the Lean environment (commit deca326).

• +2 new declarations
• −0 removed declarations

+Matrix.IsTotallyNonneg.diagonal
+Matrix.IsTotallyNonneg.diagonal_const

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No changes to strong technical debt.

No changes to weak technical debt.

Current commit deca326651
Reference commit d77ef0741c

This script lives in the mathlib-ci repository. To run it locally, from your mathlib4 directory:

git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci
../mathlib-ci/scripts/reporting/technical-debt-metrics.sh pr_summary

• The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
• The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).