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Theorems · Theorem · linear algebra

Matrix.LE.le.posSemidef

∀ {𝕜 : Type u_1} {n : Type u_2} [inst : RCLike 𝕜] {A : Matrix n n 𝕜}, 0 ≤ A → A.PosSemidef

Alias of the forward direction of Matrix.nonneg_iff_posSemidef.

Defined in
Mathlib.Analysis.Matrix.Order
Cited by
2 results in Mathlib
Foundations
Depth 168 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
RCLike
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Matrix.isStrictlyPositive_iff_posDef · cited by 2Matrix.isStrictlyPositive…Matrix.PosSemidef.inv_sqrt · cited by 0PosSemidef.inv_sqrtMatrix · cited by 4303MatrixRCLike · cited by 2829RCLikeRCLike.toPartialOrder · cited by 106RCLike.toPartialOrderMatrix.PosSemidef · cited by 76Matrix.PosSemidefMatrix.nonneg_iff_posSemidef · cited by 2Matrix.nonneg_iff_posSemi…le.posSemidefCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.