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In [[mathematics]], the '''symmetric closure''' of a [[binary relation]] <math>R</math> on a [[Set (mathematics)|set]] < ...humans and <math>R</math> is the relation 'parent of', then the symmetric closure of <math>R</math> is the relation "<math>x</math> is a parent or a child of ...

In [[mathematics]], the '''reflexive closure''' of a [[binary relation]] <math>R</math> on a [[Set (mathematics)|set]] < ...th> means "<math>x</math> is less than <math>y</math>", then the reflexive closure of <math>R</math> is the relation "<math>x</math> is less than or equal {{n ...

...fer the associated [[closure (topology)|closure]] [[operator (mathematics)|operators]] <math>\{k_i\}_{i\in I}</math> to be in non-decreasing order where <math>k | title = The closure-complement-frontier problem in saturated polytopological spaces ...

==''j''-closure== ...> is the characteristic morphism of <math>\bar s</math> which is the ''j''-closure of ''s''. The bottom two squares are pullback squares and they are containe ...

...linear operator]] ''T'' on a complex [[Hilbert space]] ''H'' such that the closure of the [[numerical range]] coincides with the [[convex hull]] of its [[spec ...&version=1.0&verb=Display&handle=euclid.pja%2F1195526397 Certain convexoid operators]'' ...

...f</math> in <math>X \times Y.</math> Such an <math>F</math> is called a '''closure of <math>f</math> in <math>X \times Y</math>''', is denoted by <math>\overl ...h>\operatorname{graph} f</math> in <math>X \times Y</math> is equal to the closure of <math>\operatorname{graph} f\big\vert_C</math> in <math>X \times Y</math ...

...lysis]]. It states that in a [[unital algebra|unital]] [[C*-algebra]], the closure of the [[convex hull]] of the [[unitary element]]s is the closed [[unit bal ...ast=Russo |first=B. |author2=H. A. Dye |year=1966|title=A Note on Unitary Operators in C*-Algebras |journal=Duke Mathematical Journal |volume=33 |pages=413–416 ...

...l|mr=0038008|last1=Kreĭn|first1=M.G.|last2=Rutman|first2=M.A.|title=Linear operators leaving invariant a cone in a Banach space|journal=Amer. Math. Soc. Transl. ...>, and <math>K-K</math> is [[dense set|dense]] in <math>X</math>, i.e. the closure of the set <math>\{u - v : u,\,v\in K\}=X</math>. <math>K</math> is also kn ...

|title=Methods of modern mathematical physics, vol. IV. Analysis of operators ...>\lambda</math> is the only point of the spectrum of <math>A</math> in the closure of <math>\Omega</math>; that is, <math>\sigma(A)\cap\overline{\Omega}=\{\la ...

|title=Introduction to the theory of linear nonselfadjoint operators Let <math>A</math> be a [[Unbounded operator#Closed linear operators|closed linear operator]] in the Banach space <math>\mathfrak{B}</math>. Let ...

...'x''** is a [[Closure operator#Closure operators on partially ordered sets|closure]]. ...

...'f''}} in {{math|''X'' ×&thinsp;''Y''}}. Such an {{mvar|F}} is called a '''closure of {{mvar|f}} in {{math|''X'' ×&thinsp;''Y''}}''', is denoted by {{math|{{o ...require that the set {{mvar|D}} be a vector subspace of {{mvar|X}} and the closure of {{mvar|f}} be a linear map. ...

...ates simultaneously. By either increasing the [[arity]] of the fixed-point operators or by nesting them, every simultaneous least, inflationary or partial fixed ==Transitive closure logic == ...

...contains all constants and separates points, then the [[Closure (topology)|closure]] of <math>A</math> is <math>\mathcal{C}(X).</math> In the case of complex The closure of <math>C_{00}(X)</math> is precisely <math>C_0(X).</math> In particular, ...

...nach fixed-point theorem can be applied to the restriction of ''f'' to the closure of ''f''(''D'') on which ''d'' defines a complete metric, defining the same ...ns, in particular the Siegel generalized disk of symmetric Hilbert-Schmidt operators with operator norm less than 1. The Earle-Hamilton theorem applies equally ...

...[[quantum states]] in the Schrödinger picture and to [[Operator (physics)|operators]] in the Heisenberg picture. ...t unitary transformations relate operators in one picture to the analogous operators in the others. Not all textbooks and articles make explicit which picture e ...

...pological vector spaces]], {{em|all}} [[Surjective map|surjective]] linear operators are necessarily almost open. ...r any neighborhood <math>U</math> of <math>0</math> in <math>X,</math> the closure of <math>T(U)</math> in <math>Y</math> is a neighborhood of the origin. ...

...In the case of L² spaces—the case treated in detail below—other operators associated with the closed curve, such as the [[Szegő kernel|Szegő projecti ==Operators on the unit circle== ...

...ows to reduce the matrix's size by some of the above-mentioned compression operators. ...As it was proven in ({{harvtxt|Knezevic|Cohen|2017}}), if the compression-closure of the class of unitary matrices contains a subset where computing this pol ...

|''t'', E', K where closure(t,E') = E[x] |Exp, E'[x=closure(Abs,E)], K ...