Positive operator (Hilbert space)
id:
positive-operator-hilbert-space-245-16837618
title:
Positive operator (Hilbert space)
text:
In mathematics as well as physics, a linear operator A acting on an inner product space is called positive-semidefinite if, for every x ∈ Dom , ⟨ A x , x ⟩ ∈ R and ⟨ A x , x ⟩ ≥ 0 , where Dom is the domain of A . Positive-semidefinite operators are denoted as A ≥ 0 . The operator is said to be positive-definite, and written A > 0 , if ⟨ A x , x ⟩ > 0 , for all x ∈ D o m ∖ { 0 } . Many authors define a positive operator A to be a self-adjoint non-negative operator. We show below that for a
brand slug:
wiki
category slug:
encyclopedia
description:
original url:
https://en.wikipedia.org/wiki/Positive_operator_(Hilbert_space)
date created:
date modified:
2024-01-03T23:28:45Z
main entity:
{"identifier":"Q2627013","url":"https://www.wikidata.org/entity/Q2627013"}
image:
fields total:
13
integrity:
13