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Theorems · Theorem · linear algebra

Matrix.PosSemidef.conjTranspose

∀ {n : Type u_2} {R : Type u_3} [inst : Ring R] [inst_1 : PartialOrder R] [inst_2 : StarRing R] {M : Matrix n n R},
  M.PosSemidef → M.conjTranspose.PosSemidef
Defined in
Mathlib.LinearAlgebra.Matrix.PosDef
Cited by
2 results in Mathlib
Foundations
Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
RingPartialOrderStarRing
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Around this declaration

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

Matrix.PosSemidef.inv · cited by 2PosSemidef.invMatrix.posSemidef_conjTranspose_iff · cited by 0Matrix.posSemidef_conjTra…Ring · cited by 7463RingPartialOrder · cited by 6410PartialOrderMatrix · cited by 4303MatrixStarRing · cited by 1686StarRingMatrix.conjTranspose · cited by 202Matrix.conjTransposeMatrix.PosSemidef · cited by 76Matrix.PosSemidefPosSemidef.conjTransposeCITED BYCITES

Cites6

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Cited by2

Results whose statement or proof uses this declaration.