Theorems · Theorem · linear algebra
Matrix.rank_unit
∀ {n : Type un} {R : Type uR} [inst : Fintype n] [inst_1 : DecidableEq n] [inst_2 : CommSemiring R]
[StrongRankCondition R] (A : (Matrix n n R)ˣ), (↑A).rank = Fintype.card n- Defined in
- Mathlib.LinearAlgebra.Matrix.Rank
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- CommSemiringstatement and proof · cited by 10,911
- Fintypestatement and proof · cited by 7,736
- Matrixstatement and proof · cited by 4,303
- Unitsstatement and proof · cited by 2,804
- le_antisymmproof · cited by 2,068
- Units.valstatement and proof · cited by 1,966
- Fintype.cardstatement · cited by 1,386
- StrongRankConditionstatement and proof · cited by 286
- mul_inv_cancelproof · cited by 128
- Matrix.rankstatement and proof · cited by 48
- Units.val_oneproof · cited by 39
- Units.val_mulproof · cited by 22
Cited by1
Results whose statement or proof uses this declaration.
- Matrix.rank_of_isUnitproof · cited by 0