Search results

...nd the relations).<ref>{{harvnb|Procesi|2007|loc=Ch. 9, § 1.4.}}</ref> The theorems are among the most important results of [[invariant theory]]. ...haracteristic (algebra)|characteristic]]-free invariant theory extends the theorems to a [[field (mathematics)|field]] of arbitrary characteristic.<ref>{{harvn ...

...[functional analysis]]. It states that in a [[unital algebra|unital]] [[C*-algebra]], the closure of the [[convex hull]] of the [[unitary element]]s is the cl ...A. Belfi | title = Characterizations of C*-Algebras: The Gelfand–Naimark Theorems | publisher = Marcel Dekker | location = New York | year = 1986 | isbn = 0- ...

{{Short description|Subset T of a topological vector space X where the linear span of T is a dense subset of X}} ...ath>X</math> is said to be a '''total''' subset of <math>X</math> if the [[linear span]] of <math>T</math> is a [[Dense set|dense subset]] of <math>X.</math> ...

...somorphism]] from <math>\mathfrak g</math> to itself, that is, a bijective linear map preserving the Lie bracket. The set of automorphisms of <math>\mathfrak ...operatorname{Aut}^0(\mathfrak{g})</math>. These form a [[normal subgroup]] in the group of automorphisms, and the [[quotient group|quotient]] <math>\oper ...

{{Short description|Concept in Algebra}}In [[algebra]], more specifically [[group theory]], a ''p''-'''elementary group''' is a ...rem on induced characters]] states that a character on a finite group is a linear combination with integer coefficients of characters [[induced character|ind ...

...tation of the symmetric group]] <math>S_n</math> to be zero. It was proven in 1988 by Carlos Gamas.<ref name="Gamas">{{cite journal |journal=Linear Algebra and Its Applications ...

In [[linear algebra]], let {{math|1=''A''&nbsp;=&nbsp;(''a_ij'')}} be a {{math|''n'' ...55-1 |edition=2nd |page=92 |chapter=Basic Iterative Methods and Comparison Theorems}}</ref> ...

{{Short description|Theorem of operator algebra}} ...n algebras]] and so-called domains of positivity. Thus it links [[operator algebra]]ic and [[Convex function|convex]] [[Order theory|order theoretic]] views o ...

{{short description|Identity in algebra useful for evaluating certain types of determinants}} ...f Sylvester's (determinant) identity | journal = Mathematics and Computers in Simulation | volume = 42 | issue = 4–6 | page = 585 | year = 1996 }}</ref> ...

...e [[complex number]]s <math>\mathbb{C}</math>) to linear operators valued in [[topological vector space]]s (TVSs). ...nd {{math|L(''X''; ''Y'')}} will denote the vector space of all continuous linear maps from {{mvar|X}} to {{mvar|Y}}, where if {{mvar|X}} and {{mvar|Y}} are ...

{{Short description|Number of solutions of linear systems in terms of matrix ranks}} ...|solutions]] of a [[system of linear equations]], given the [[Rank (linear algebra)|rank]]s of its [[augmented matrix]] and [[coefficient matrix]]. The theore ...

{{Short description|Formula in representation theory}} ...an [[irreducible representation]] of a semisimple complex [[Lie algebra]] in a [[tensor product]] of two [[irreducible representation]]s. ...

In [[mathematics]], at the intersection of [[algebraic topology]] and [[algebr ...left <math>A</math>-module <math>M</math> together with an <math>A</math>-linear map<blockquote><math>\psi: M \to \Gamma\otimes_AM</math></blockquote>which ...

{{Short description|Theorem on linear operators}} ...and [[matrix theory]] about the representation of a sum of two bounded, [[linear operators]] (resp. matrices). The theorem was proven by [[Theodore Motzkin] ...

...ntrol]], and [[mathematical economics]].<ref>{{cite book|title=Fixed Point Theorems with Applications to Economics and Game Theory|last=Border|first=Kim C.|pub : <math>\forall x \in X: \,\,\, f(x) \in F(x) \,.</math> ...

...etermination of the inertia of a partitioned Hermitian matrix", ''[[Linear Algebra and its Applications]]'', volume 1 (1968), pages 73–81</ref> : <math> \mathrm{In}(H) = \left( \pi(H), \nu(H), \delta(H) \right) </math> ...

The '''Stein-Rosenberg theorem''', proved in 1948, states that under certain premises, the [[Jacobi method]] and the [[G Let <math>A=(a_{ij})\in\mathbb{R}^{n\times n}</math>. Let <math>\rho(X)</math> be the [[spectral ra ...

...996|loc=Theorem 7.2.6.}}</ref><ref name="9.4 and 9.5">{{harvnb|Hall|2015}} Theorems 9.4 and 9.5</ref> There is a closely related theorem classifying the [[Comp ...difference between the two results is in the precise notion of "integral" in the definition of a dominant integral element. If <math>K</math> is simply ...

...general functions by functions of special form, such as [[polynomial]]s. In more recent work, the convergence of a sequence of operators is studied: th ...sequence of real numbers tending to zero. Then there exists a point ''x'' in ''X'' such that the distance of ''x'' to ''V''_''i'' is exactly < ...

In the mathematical theory of [[free probability]], the notion of '''free inde ...ontext of Voiculescu's free probability theory, many classical-probability theorems or phenomena have free probability analogs: the same theorem or phenomenon ...