Theorems · Theorem · linear algebra
Matrix.rank_of_isUnit
∀ {n : Type un} {R : Type uR} [inst : Fintype n] [inst_1 : DecidableEq n] [inst_2 : CommSemiring R]
[StrongRankCondition R] (A : Matrix n n R), IsUnit A → A.rank = Fintype.card n- Defined in
- Mathlib.LinearAlgebra.Matrix.Rank
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
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
- Unitsproof · cited by 2,804
- Units.valproof · cited by 1,966
- IsUnitstatement and proof · cited by 1,602
- Fintype.cardstatement · cited by 1,386
- StrongRankConditionstatement and proof · cited by 286
- Matrix.rankstatement · cited by 48
- Matrix.rank_unitproof · cited by 1
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