Theorems · Definition · linear algebra

Matrix.PosSemidef

{n : Type u_2} → {R : Type u_3} → [inst : Ring R] → [PartialOrder R] → [StarRing R] → Matrix n n R → Prop

A matrix M : Matrix n n R is positive semidefinite if it is Hermitian and xᴴ * M * x is nonnegative for all x of finite support.

Defined in

Mathlib.LinearAlgebra.Matrix.PosDef

Cited by

76 results in Mathlib

Foundations

Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingPartialOrderStarRing