Theorems · Theorem · linear algebra
Matrix.rank_self_mul_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 * A.conjTranspose).rank = A.rank- Defined in
- Mathlib.LinearAlgebra.Matrix.Rank
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
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- 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
- StarRingstatement and proof · cited by 1,686
- StarOrderedRingstatement and proof · cited by 587
- Matrix.conjTransposestatement and proof · cited by 202
- Matrix.rankstatement and proof · cited by 48
- Matrix.conjTranspose_conjTransposeproof · cited by 31
- Matrix.rank_conjTranspose_mul_selfproof · cited by 2
- Matrix.rank_conjTransposeproof · cited by 1
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