Theorems · Theorem · linear algebra
Matrix.rank_mul_le_left
∀ {m : Type um} {n : Type un} {o : Type uo} {R : Type uR} [inst : Fintype n] [inst_1 : Fintype o]
[inst_2 : CommSemiring R] [StrongRankCondition R] (A : Matrix m n R) (B : Matrix n o R), (A * B).rank ≤ A.rank- Defined in
- Mathlib.LinearAlgebra.Matrix.Rank
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHom.idproof · cited by 18,349
- CommSemiringstatement and proof · cited by 10,911
- LinearMapproof · cited by 10,215
- Fintypestatement and proof · cited by 7,736
- Matrixstatement and proof · cited by 4,303
- Nontrivialproof · cited by 2,416
- Module.finrankproof · cited by 1,770
- LinearMap.rangeproof · cited by 893
- StrongRankConditionstatement and proof · cited by 286
- Matrix.rankstatement and proof · cited by 48
- Matrix.mulVecLinproof · cited by 38
- Module.rank_lt_aleph0proof · cited by 23
Cited by5
Results whose statement or proof uses this declaration.
- Matrix.rank_mul_eq_left_of_det_mem_nonZeroDivisorsproof · cited by 2
- Matrix.rank_conjTransposeproof · cited by 1
- Matrix.rank_unitproof · cited by 1
- Matrix.rank_mul_leproof · cited by 0
- Matrix.rank_vecMulVec_leproof · cited by 0