Theorems · Theorem · linear algebra
Matrix.isRegular_of_isLeftRegular_det
∀ {n : Type v} {α : Type w} [inst : DecidableEq n] [inst_1 : Fintype n] [inst_2 : CommRing α] {A : Matrix n n α},
IsLeftRegular A.det → IsRegular A- Defined in
- Mathlib.LinearAlgebra.Matrix.Adjugate
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 99 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.
Cites15
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
- Matrix.detstatement and proof · cited by 665
- IsRegularstatement · cited by 116
- IsLeftRegularstatement and proof · cited by 97
- Matrix.adjugateproof · cited by 64
- Matrix.mul_assocproof · cited by 56
- Matrix.mul_oneproof · cited by 45
- Matrix.one_mulproof · cited by 30
- Matrix.mul_smulproof · cited by 14
- Matrix.smul_mulproof · cited by 11
Cited by3
Results whose statement or proof uses this declaration.
- Matrix.adjugate_mul_distrib_auxproof · cited by 1
- Matrix.SemiconjBy.zpow_rightproof · cited by 1
- Matrix.IsHadamard.of_mul_conjTransposeproof · cited by 1