Mathlib Map

Theorems · Theorem · linear algebra

Matrix.TransvectionStruct.det_toMatrix_prod

∀ {n : Type u_1} {R : Type u₂} [inst : DecidableEq n] [inst_1 : CommRing R] [inst_2 : Fintype n]
  (L : List (Matrix.TransvectionStruct n R)), (List.map Matrix.TransvectionStruct.toMatrix L).prod.det = 1
Defined in
Mathlib.LinearAlgebra.Matrix.Transvection
Cited by
2 results in Mathlib
Foundations
Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
DecidableEqCommRingFintype
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Matrix.SpecialLinearGroup.exists_list_transvec_mul_diagonal_mul_list_transvec · cited by 1SpecialLinearGroup.exists…Matrix.diagonal_transvection_induction · cited by 1Matrix.diagonal_transvect…CommRing · cited by 17173CommRingFintype · cited by 7736FintypeMatrix · cited by 4303Matrixmul_one · cited by 3885mul_oneMatrix.det · cited by 665Matrix.detMatrix.det.congr_simp · cited by 91det.congr_simpMatrix.det_mul · cited by 51Matrix.det_mulMatrix.TransvectionStruct · cited by 42Matrix.TransvectionStructMatrix.det_one · cited by 35Matrix.det_oneMatrix.TransvectionStruct.toMatrix · cited by 32TransvectionStruct.toMatr…Matrix.TransvectionStruct.det · cited by 4TransvectionStruct.detTransvectionStruct.det_toMatr…CITED BYCITES

Cites11

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.