Theorems · Theorem · linear algebra
Matrix.rank_of_det_ne_zero
∀ {m : Type um} {R : Type u_1} [inst : CommRing R] [IsDomain R] [inst_2 : Fintype m] [inst_3 : DecidableEq m]
{A : Matrix m m R}, A.det ≠ 0 → A.rank = Fintype.card m- Defined in
- Mathlib.LinearAlgebra.Matrix.Rank
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- IsDomainstatement and proof · cited by 2,196
- Fintype.cardstatement · cited by 1,386
- Matrix.detstatement and proof · cited by 665
- Matrix.rankstatement · cited by 48
- mem_nonZeroDivisors_of_ne_zeroproof · cited by 34
- Matrix.rank_of_det_mem_nonZeroDivisorsproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Matrix.IsPivotedBy.rank_eqproof · cited by 1