feat(LinearAlgebra/Transvection/Basic): define dilatransvections

[AntoineChambert-Loir]

Define LinearEquiv.dilatransvections.
These are linear equivalences whose associated linear map is a transvection.
This definition has the interest of being usable without any assumption on the base ring.
Over a division ring, they correspond exactly to those linear equivalences e such that e - LinearMap.id has rank at most one.

They (will) appear in Dieudonné's theorem that describes the generation of elements of the general linear group as products of several transvections and one additional dilatransvection.

---

[github-actions]

PR summary d68c4dc09f

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.LinearAlgebra.Transvection	1390	1332	-58 (-4.17%)

Import changes for all files

Files	Import difference
Mathlib.LinearAlgebra.Transvection	-58

---

Declarations diff

+ IsBaseChange.transvection
+ LinearEquiv.dilatransvection.baseChange
+ LinearEquiv.transvection.baseChange
+ LinearMap.transvection.baseChange
+ dilatransvections
+ dilatransvections_pow_mono
+ inv_eq
+ inv_eq'
+ inv_mem_dilatransvections_iff
+ inv_mem_transvections_iff
+ mem_dilatransvections_iff_finrank
+ mem_dilatransvections_iff_rank
+ mem_transvections
+ mem_transvections_iff
+ one_mem_dilatransvections
+ one_mem_transvections
+ refl_mem_dilatransvections
+ refl_mem_transvections
+ symm_mem_dilatransvections_iff
+ symm_mem_transvections_iff
+ transvections
+ transvections_pow_mono
+ transvections_subset_dilatransvections
- _root_.IsBaseChange.transvection
- _root_.LinearEquiv.transvection.baseChange
- baseChange

You can run this locally as follows

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

## more verbose report:
./scripts/declarations_diff.sh long <optional_commit>

The doc-module for script/declarations_diff.sh contains some details about this script.

---

No changes to technical debt.

You can run this locally as

./scripts/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).