Theorems · Theorem · linear algebra
Matrix.TransvectionStruct.mul_inv
∀ {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 * t.inv.toMatrix = 1- Cited by
- 2 results in Mathlib
- Foundations
- Depth 83 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.
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 · cited by 4,303
- add_neg_cancelproof · cited by 213
- Matrix.TransvectionStructstatement and proof · cited by 42
- Matrix.TransvectionStruct.toMatrixstatement · cited by 32
- Matrix.transvectionproof · cited by 24
- Matrix.TransvectionStruct.invstatement · cited by 11
- Matrix.TransvectionStruct.casesOnproof · cited by 6
- Matrix.TransvectionStruct.inv_cproof · cited by 2
- Matrix.TransvectionStruct.inv_iproof · cited by 2
- Matrix.TransvectionStruct.inv_jproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Matrix.TransvectionStruct.prod_mul_reverse_inv_prodproof · cited by 2
- Matrix.GeneralLinearGroup.mem_center_iff_val_mem_range_scalarproof · cited by 2