feat(LinearAlgebra/Matrix): add Sylvester's rank inequality

[yuanyi-350]

No description provided.

[github-actions]

PR summary ebf91179b4

Import changes exceeding 2%

%	File
+2.06%	Mathlib.LinearAlgebra.Matrix.Rank

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.LinearAlgebra.Matrix.Rank	1604	1637	+33 (+2.06%)

Import changes for all files

Files	Import difference
Mathlib.Algebra.Lie.Classical Mathlib.LinearAlgebra.SymplecticGroup	4
Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.Card	17
6 files Mathlib.Combinatorics.Configuration Mathlib.LinearAlgebra.Matrix.Echelon.Decomposition Mathlib.LinearAlgebra.Matrix.Echelon.Pivot Mathlib.LinearAlgebra.Matrix.Rank Mathlib.Tactic.Echelon.Bareiss Mathlib.Tactic.NormRank	33

---

Declarations diff (regex)

+ rank_mul_ge

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)

✅ Lean-aware diff — post-build, computed from the Lean environment (commit ebf9117).

• +1 new declarations
• −0 removed declarations

+Matrix.rank_mul_ge

---

No changes to strong technical debt.
No changes to weak technical debt.

Current commit ebf91179b4
Reference commit 863e60949d

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.py 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).