Theorems · Theorem · group theory
Matrix.SpecialLinearGroup.transvection_mulVec_single_other
Deprecated since 2026-06-22Use Matrix.SpecialLinearGroup.transvection_smul_single_snd instead.
∀ {ι : Type u_1} {F : Type u_2} [inst : DecidableEq ι] [inst_1 : Fintype ι] [inst_2 : CommRing F] {i j : ι}
(hij : i ≠ j) (b : F),
(↑(Matrix.SpecialLinearGroup.transvection hij b)).mulVec (Pi.single j 1) = Pi.single j 1 + b • Pi.single i 1- Cited by
- 0 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqFintypeCommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Fintypestatement and proof · cited by 7,736
- Matrixstatement and proof · cited by 4,303
- mul_oneproof · cited by 3,885
- Matrix.detstatement · cited by 665
- Pi.singlestatement and proof · cited by 518
- Matrix.mulVecstatement and proof · cited by 267
- Pi.single_eq_sameproof · cited by 144
- Matrix.singleproof · cited by 129
- Matrix.SpecialLinearGroup.transvectionstatement · cited by 21
- Matrix.one_mulVecproof · cited by 12
- Matrix.add_mulVecproof · cited by 7
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