Theorems · Theorem · linear algebra
Matrix.rank_add_rank_le_card_of_mul_eq_zero
∀ {l : Type ul} {m : Type um} {n : Type un} {R : Type uR} [inst : Fintype n] [inst_1 : Field R] [Finite l]
[inst_3 : Fintype m] {A : Matrix l m R} {B : Matrix m n R}, A * B = 0 → A.rank + B.rank ≤ Fintype.card m- Defined in
- Mathlib.LinearAlgebra.Matrix.Rank
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- RingHom.idproof · cited by 18,349
- LinearMapproof · cited by 10,215
- Fintypestatement and proof · cited by 7,736
- Fieldstatement and proof · cited by 7,404
- Matrixstatement and proof · cited by 4,303
- Finitestatement and proof · cited by 3,029
- Module.finrankproof · cited by 1,770
- map_zeroproof · cited by 1,614
- Module.Basisproof · cited by 1,477
- Fintype.cardstatement and proof · cited by 1,386
- LinearMap.rangeproof · cited by 893
Cited by1
Results whose statement or proof uses this declaration.
- Configuration.ofField.crossProduct_eq_zero_of_dotProduct_eq_zeroproof · cited by 1