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

mathematics (specifically linear algebra, operator theory, and functional analysis) as well as physics, a linear operator A {\displaystyle A} acting...

continuous linear operator or continuous linear mapping is a continuous linear transformation between topological vector spaces. An operator between two...

functional analysis, a positive linear functional on an ordered vector space ( V , ≤ ) {\displaystyle (V,\leq )} is a linear functional f {\displaystyle...

In functional analysis and operator theory, a bounded linear operator is a linear transformation L : X → Y {\displaystyle L:X\to Y} between topological...

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

a linear endomorphism. Sometimes the term linear operator refers to this case, but the term "linear operator" can have different meanings for different...

the object. A projection on a vector space V {\displaystyle V} is a linear operator P : V → V {\displaystyle P\colon V\to V} such that P 2 = P {\displaystyle...

"operator" should be understood as "linear operator" (as in the case of "bounded operator"); the domain of the operator is a linear subspace, not necessarily the...

In functional analysis, a branch of mathematics, a compact operator is a linear operator T : X → Y {\displaystyle T:X\to Y} , where X , Y {\displaystyle...

time series analysis, the shift operator is called the lag operator. Shift operators are examples of linear operators, important for their simplicity...

functional analysis, a normal operator on a complex Hilbert space H {\displaystyle H} is a continuous linear operator N : H → H {\displaystyle N\colon...

isomorphism between Hilbert spaces. Definition 1. A unitary operator is a bounded linear operator U : H → H on a Hilbert space H that satisfies U*U = UU*...

In mathematical analysis, an integral linear operator is a linear operator T given by integration; i.e., ( T f ) ( x ) = ∫ f ( y ) K ( x , y ) d y {\displaystyle...

example of a sublinear function (in fact, it is even a linear functional) that is neither positive nor a seminorm; the same is true of this map's negation...

generally solve elliptic equations. Let L {\displaystyle L} be a linear differential operator of order m on a domain Ω {\displaystyle \Omega } in Rn given...

the trace of a linear operator mapping a finite-dimensional vector space into itself, since all matrices describing such an operator with respect to...

mathematics, specifically functional analysis, a trace-class operator is a linear operator for which a trace may be defined, such that the trace is a finite...

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 operator...

bounded linear operators on a Banach space X. Let ( T n ) n ∈ N {\displaystyle (T_{n})_{n\in \mathbb {N} }} be a sequence of linear operators on the Banach...

second-order differential operator, the Laplace operator maps Ck functions to Ck−2 functions for k ≥ 2. It is a linear operator Δ : Ck(Rn) → Ck−2(Rn), or...

a positive linear operator (density matrix) acting on H. A linear map Φ: L(H2) → L(H1) is said to be positive if it preserves the cone of positive elements...

In linear algebra (and its application to quantum mechanics), a raising or lowering operator (collectively known as ladder operators) is an operator that...

self-adjoint operator on a complex vector space V with inner product ⟨ ⋅ , ⋅ ⟩ {\displaystyle \langle \cdot ,\cdot \rangle } is a linear map A (from V...

In mathematics, a linear form (also known as a linear functional, a one-form, or a covector) is a linear map from a vector space to its field of scalars...

A Jacobi operator, also known as Jacobi matrix, is a symmetric linear operator acting on sequences which is given by an infinite tridiagonal matrix. It...

In operator theory, a bounded operator T on a Banach space is said to be nilpotent if Tn = 0 for some positive integer n. It is said to be quasinilpotent...

of two linear operators is a linear operator, as well as the product (on the left) of a linear operator by a differentiable function, the linear differential...

In logic, linear temporal logic or linear-time temporal logic (LTL) is a modal temporal logic with modalities referring to time. In LTL, one can encode...

mathematics, a finite-rank operator is a bounded linear operator between Banach spaces whose range is finite-dimensional. Finite-rank operators are matrices (of...