{\displaystyle A} . Positive-semidefinite operators are denoted as A ≥ 0 {\displaystyle A\geq 0} . The operator is said to be positive-definite, and written...

information science, a positive operator-valued measure (POVM) is a measure whose values are positive semi-definite operators on a Hilbert space. POVMs...

With positive control, an activator protein stimulates transcription by binding to DNA (usually at a site other than the operator). In positive inducible...

mathematics, operator theory is the study of linear operators on function spaces, beginning with differential operators and integral operators. The operators may...

containing negation Positive number, a number that is greater than 0 Plus sign, the sign "+" used to indicate a positive number Positive operator, a type of linear...

Benjamin; Moran, Bill; Cochran, Doug (2021). "Positive operator-valued measures and densely defined operator-valued frames". Rocky Mountain Journal of Mathematics...

The notion comes from functional analysis where positive semidefinite matrices define positive operators. If two matrices A {\displaystyle A} and B {\displaystyle...

the polar decomposition of A. The positive operator P is the unique positive square root of the positive operator A∗A, and U is defined by U = AP−1....

In operator theory, Naimark's dilation theorem is a result that characterizes positive operator valued measures. It can be viewed as a consequence of Stinespring's...

Positive-definite kernel Positive-definite matrix Positive-definite operator Positive-definite quadratic form Fasshauer, Gregory E. (2011), "Positive definite kernels:...

mathematics, positive semidefinite may refer to: Positive semidefinite function Positive semidefinite matrix Positive semidefinite operator Positive semidefinite...

transform is replaced by self-adjointness for positive operators. Theorem—A symmetric positive operator A {\displaystyle A} is self-adjoint if and only...

a − 1 {\displaystyle b^{-1}\leq a^{-1}} holds. Nonnegative matrix Positive operator (Hilbert space) Palmer 2001, p. 798. Blackadar 2006, p. 63. Kadison...

In mathematics, more specifically in functional analysis, a positive linear operator from an preordered vector space ( X , ≤ ) {\displaystyle (X,\leq )}...

orthonormal basis and A : H → H {\displaystyle A:H\to H} a positive bounded linear operator on H {\displaystyle H} . The trace of A {\displaystyle A} is...

projective measurements.[clarification needed] They are generalized by positive operator valued measures (POVMs) in the same sense that a mixed state or density...

relevant operators O {\displaystyle {\mathcal {O}}} on a Hilbert space H {\displaystyle {\mathcal {H}}} and to construct a positive operator H as a quantum...

Hidden-variable models have been constructed for Werner states even if positive operator-valued measurements (POVM) are allowed, not only von Neumann measurements...

{\displaystyle N^{\ast }=N} skew-Hermitian operators: N ∗ = − N {\displaystyle N^{\ast }=-N} positive operators: N = M ∗ M {\displaystyle N=M^{\ast }M} for...

coefficients Metzler matrix (Quasipositive matrix) Positive operator – In mathematics, a linear operator acting on inner product space Krein–Rutman theorem –...

theory and operator theory, the Choi–Jamiołkowski isomorphism refers to the correspondence between quantum channels (described by completely positive maps)...

In operator theory, a branch of mathematics, a positive-definite kernel is a generalization of a positive-definite function or a positive-definite matrix...

to the identity operator on H {\displaystyle H} . A state on a C ∗ {\displaystyle C^{*}} -algebra A {\displaystyle A} is a positive linear functional...

measure on [0, ∞). Compact operator on Hilbert space Unbounded operator Hermitian adjoint Normal operator Positive operator Helffer–Sjöstrand formula The...

density operator; Such quantum state is known as a mixed state. The density operator of a mixed state is a trace class, nonnegative (positive semi-definite)...

2022-05-22. "Operators". Microsoft. 30 June 2021. Retrieved 2021-07-19. The % operator is defined only in cases where either both sides are positive or both...

operators. Positive normal functional are those that are non-negative on positive operators. For every non-zero operator, there is a positive normal functional...

generalized using positive-operator-valued measures (POVM). A POVM is a measure whose values are positive semi-definite operators on a Hilbert space...

partial differential equations, elliptic operators are differential operators that generalize the Laplace operator. They are defined by the condition that...

replaced by a density matrix, and the projection operators are to be replaced by positive operator valued measures. More precisely, a quantum Markov...