Theorems · Theorem · linear algebra
Matrix.TransvectionStruct.det
∀ {n : Type u_1} {R : Type u₂} [inst : DecidableEq n] [inst_1 : CommRing R] [inst_2 : Fintype n]
(t : Matrix.TransvectionStruct n R), t.toMatrix.det = 1- Cited by
- 4 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqCommRingFintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Matrix.detstatement · cited by 665
- Matrix.TransvectionStructstatement and proof · cited by 42
- Matrix.TransvectionStruct.toMatrixstatement · cited by 32
- Matrix.TransvectionStruct.iproof · cited by 7
- Matrix.TransvectionStruct.jproof · cited by 6
- Matrix.TransvectionStruct.cproof · cited by 5
- Matrix.TransvectionStruct.hijproof · cited by 4
- Matrix.det_transvection_of_neproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- Matrix.SpecialLinearGroup.scalar_eq_self_of_mem_centerproof · cited by 2
- Matrix.TransvectionStruct.det_toMatrix_prodproof · cited by 2
- Matrix.diagonal_transvection_induction_of_det_ne_zeroproof · cited by 1
- Real.map_matrix_volume_pi_eq_smul_volume_piproof · cited by 1