Theorems · Theorem · linear algebra
Matrix.rank_transpose_mul_self
∀ {m : Type um} {n : Type un} {R : Type uR} [inst : Fintype n] [inst_1 : Fintype m] [inst_2 : Field R]
[inst_3 : LinearOrder R] [IsStrictOrderedRing R] (A : Matrix m n R), (A.transpose * A).rank = A.rank- Defined in
- Mathlib.LinearAlgebra.Matrix.Rank
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 118 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.
- LinearOrderstatement and proof · cited by 8,572
- Fintypestatement and proof · cited by 7,736
- Fieldstatement and proof · cited by 7,404
- Submoduleproof · cited by 7,192
- Matrixstatement and proof · cited by 4,303
- IsStrictOrderedRingstatement and proof · cited by 2,490
- Module.finrankproof · cited by 1,770
- LinearMap.rangeproof · cited by 893
- LinearMap.kerproof · cited by 848
- Matrix.transposestatement and proof · cited by 389
- add_left_injectiveproof · cited by 49
- Matrix.rankstatement · cited by 48
Cited by1
Results whose statement or proof uses this declaration.
- Matrix.rank_self_mul_transposeproof · cited by 0