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Theorems · Theorem · linear algebra

Matrix.lift_cRank_submatrix_le

∀ {m : Type um} {m₀ : Type um₀} {n : Type un} {n₀ : Type un₀} {R : Type uR} [inst : Semiring R] (A : Matrix m n R)
  (r : m₀ → m) (c : n₀ → n),
  Cardinal.lift.{um, max uR um₀} (A.submatrix r c).cRank ≤ Cardinal.lift.{um₀, max uR um} A.cRank
Defined in
Mathlib.LinearAlgebra.Matrix.Rank
Cited by
3 results in Mathlib
Foundations
Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Semiring
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Around this declaration

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Matrix.lift_cRank_submatrix · cited by 3Matrix.lift_cRank_submatr…Matrix.cRank_submatrix_le · cited by 0Matrix.cRank_submatrix_leMatrix.eRank_submatrix_le · cited by 0Matrix.eRank_submatrix_leDFunLike.coe · cited by 62936DFunLike.coeRingHom.id · cited by 18349RingHom.idSemiring · cited by 13802SemiringLinearMap · cited by 10215LinearMapSubmodule · cited by 7192SubmoduleSet.image · cited by 5609Set.imageSet.range · cited by 4705Set.rangeMatrix · cited by 4303MatrixSet.univ · cited by 3945Set.univEquiv.symm · cited by 3681Equiv.symmLE.le.trans · cited by 3151le.transCardinal · cited by 2598CardinalSubmodule.span · cited by 1504Submodule.spanSubmodule.map · cited by 614Submodule.mapCardinal.lift · cited by 583Cardinal.liftMatrix.lift_cRank_submatrix_leCITED BYCITES

Cites31

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Cited by3

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