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Theorems · Theorem · linear algebra

Matrix.PosDef.transpose_iff

∀ {n : Type u_2} {R' : Type u_4} [inst : CommRing R'] [inst_1 : PartialOrder R'] [inst_2 : StarRing R']
  {M : Matrix n n R'}, M.transpose.PosDef ↔ M.PosDef
Defined in
Mathlib.LinearAlgebra.Matrix.PosDef
Cited by
1 results in Mathlib
Foundations
Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingPartialOrderStarRing
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Around this declaration

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

RootPairing.Base.exists_cartanMatrix_diagaonal_mul_posDef · cited by 1Base.exists_cartanMatrix_…CommRing · cited by 17173CommRingPartialOrder · cited by 6410PartialOrderMatrix · cited by 4303MatrixStarRing · cited by 1686StarRingMatrix.transpose · cited by 389Matrix.transposeMatrix.PosDef · cited by 68Matrix.PosDefMatrix.transpose_transpose · cited by 33Matrix.transpose_transposeMatrix.PosDef.transpose · cited by 2PosDef.transposePosDef.transpose_iffCITED BYCITES

Cites8

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Cited by1

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