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Theorems · Theorem · linear algebra

Matrix.nonneg_iff_posSemidef

∀ {𝕜 : Type u_1} {n : Type u_2} [inst : RCLike 𝕜] {A : Matrix n n 𝕜}, 0 ≤ A ↔ A.PosSemidef
Defined in
Mathlib.Analysis.Matrix.Order
Cited by
2 results in Mathlib
Foundations
Depth 167 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
RCLike
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Around this declaration

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

Matrix.PosSemidef.nonneg · cited by 7PosSemidef.nonnegMatrix.LE.le.posSemidef · cited by 2le.posSemidefMatrix · cited by 4303MatrixRCLike · cited by 2829RCLikesub_zero · cited by 938sub_zeroRCLike.toPartialOrder · cited by 106RCLike.toPartialOrderMatrix.PosSemidef · cited by 76Matrix.PosSemidefMatrix.le_iff · cited by 1Matrix.le_iffMatrix.nonneg_iff_posSemidefCITED BYCITES

Cites6

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Cited by2

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