feat(LinearAlgebra): unimodular elements and completion to a basis

[xroblot]

Add a new file Mathlib/LinearAlgebra/Unimodular.lean about unimodular
elements of a module (those on which some linear functional takes the value
1).

Main results:

• Module.Basis.span_repr_eq_top_iff: v is unimodular iff its coordinates in
  a basis generate the unit ideal;
• Module.Free.exists_basis_apply_zero_eq: a unimodular vector of a rank-two
  free module completes to a basis;
• Module.Basis.span_repr_one_eq_top / Module.Free.exists_linearMap_apply_one_eq_one:
  1 is unimodular in a nonzero free algebra.

Some of the mathematics and proofs in this file were developed with the help of Claude 🤖.

[github-actions]

PR summary 37a6ec307d

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.LinearAlgebra.Unimodular (new file)	1662

---

Declarations diff (regex)

+ exists_basis_apply_zero_eq
+ exists_linearMap_apply_one_eq_one
+ span_repr_eq_top_iff
+ span_repr_one_eq_top

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 37a6ec3).

• +5 new declarations
• −0 removed declarations

+Matrix.toLinearEquiv.congr_simp
+Module.Basis.span_repr_eq_top_iff
+Module.Basis.span_repr_one_eq_top
+Module.Free.exists_basis_apply_zero_eq
+Module.Free.exists_linearMap_apply_one_eq_one

---

No changes to strong technical debt.

No changes to weak technical debt.

Current commit 37a6ec307d
Reference commit b2418b0404

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).