Theorems · Theorem · linear algebra
Matrix.rank_mul_le
∀ {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 ≤ min A.rank B.rank- Defined in
- Mathlib.LinearAlgebra.Matrix.Rank
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
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- CommSemiringstatement and proof · cited by 10,911
- Fintypestatement and proof · cited by 7,736
- Matrixstatement and proof · cited by 4,303
- StrongRankConditionstatement and proof · cited by 286
- Matrix.rankstatement · cited by 48
- le_minproof · cited by 21
- Matrix.rank_mul_le_leftproof · cited by 5
- Matrix.rank_mul_le_rightproof · cited by 2
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