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Theorems · Theorem · linear algebra

Matrix.PosDef.isHermitian

∀ {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.PosDef → M.IsHermitian
Defined in
Mathlib.LinearAlgebra.Matrix.PosDef
Cited by
4 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.PosDef.add_posSemidef · cited by 2PosDef.add_posSemidefMatrix.PosDef.eigenvalues_pos · cited by 1PosDef.eigenvalues_posMatrix.PosDef.det_pos · cited by 0PosDef.det_posMatrix.PosDef.hadamard · cited by 0PosDef.hadamardRing · cited by 7463RingPartialOrder · cited by 6410PartialOrderMatrix · cited by 4303MatrixStarRing · cited by 1686StarRingMatrix.IsHermitian · cited by 126Matrix.IsHermitianMatrix.PosDef · cited by 68Matrix.PosDefPosDef.isHermitianCITED BYCITES

Cites6

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Cited by4

Results whose statement or proof uses this declaration.