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Theorems · Theorem · linear algebra

Matrix.nondegenerate_iff_separatingRight

∀ {n : Type u_1} {A : Type u_4} [inst : CommRing A] [IsDomain A] {M : Matrix n n A} [inst_2 : Finite n],
  M.Nondegenerate ↔ M.SeparatingRight
Defined in
Mathlib.LinearAlgebra.Matrix.ToLinearEquiv
Cited by
2 results in Mathlib
Foundations
Depth 128 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingIsDomainFinite
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Matrix.separatingLeft_iff_separatingRight · cited by 2Matrix.separatingLeft_iff…Matrix.SeparatingRight.nondegenerate · cited by 0SeparatingRight.nondegene…CommRing · cited by 17173CommRingFintype · cited by 7736FintypeMatrix · cited by 4303MatrixFinite · cited by 3029FiniteIsDomain · cited by 2196IsDomainMatrix.det · cited by 665Matrix.detFintype.ofFinite · cited by 255Fintype.ofFiniteMatrix.Nondegenerate · cited by 49Matrix.NondegenerateMatrix.SeparatingRight · cited by 35Matrix.SeparatingRightMatrix.nondegenerate_iff_det_ne_zero · cited by 13Matrix.nondegenerate_iff_…Matrix.separatingRight_iff_det_ne_zero · cited by 3Matrix.separatingRight_if…Matrix.nondegenerate_iff_sepa…CITED BYCITES

Cites11

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Cited by2

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