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Theorems · Theorem · linear algebra

Matrix.PosDef.add

∀ {m : Type u_1} {R : Type u_3} [inst : Ring R] [inst_1 : PartialOrder R] [inst_2 : StarRing R] [AddLeftMono R]
  {A B : Matrix m m R}, A.PosDef → B.PosDef → (A + B).PosDef
Defined in
Mathlib.LinearAlgebra.Matrix.PosDef
Cited by
1 results in Mathlib
Foundations
Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
RingPartialOrderStarRingAddLeftMono
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Around this declaration

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

Matrix.posDef_sum · cited by 0Matrix.posDef_sumRing · cited by 7463RingPartialOrder · cited by 6410PartialOrderMatrix · cited by 4303MatrixStarRing · cited by 1686StarRingAddLeftMono · cited by 687AddLeftMonoMatrix.PosDef · cited by 68Matrix.PosDefMatrix.PosDef.posSemidef · cited by 5PosDef.posSemidefMatrix.PosDef.add_posSemidef · cited by 2PosDef.add_posSemidefPosDef.addCITED BYCITES

Cites8

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Cited by1

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