Theorems · Theorem · linear algebra
Matrix.rank_conjTranspose
∀ {m : Type um} {n : Type un} {R : Type uR} [inst : Fintype n] [inst_1 : Fintype m] [inst_2 : Field R]
[inst_3 : PartialOrder R] [inst_4 : StarRing R] [StarOrderedRing R] (A : Matrix m n R), A.conjTranspose.rank = A.rankTODO: prove this in greater generality.
- 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.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fintypestatement and proof · cited by 7,736
- Fieldstatement and proof · cited by 7,404
- PartialOrderstatement and proof · cited by 6,410
- Matrixstatement and proof · cited by 4,303
- le_antisymmproof · cited by 2,068
- StarRingstatement and proof · cited by 1,686
- StarOrderedRingstatement and proof · cited by 587
- LE.le.trans_eqproof · cited by 328
- Matrix.conjTransposestatement and proof · cited by 202
- Eq.trans_leproof · cited by 155
- Matrix.rankstatement and proof · cited by 48
- Matrix.conjTranspose_conjTransposeproof · cited by 31
Cited by1
Results whose statement or proof uses this declaration.
- Matrix.rank_self_mul_conjTransposeproof · cited by 0