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...ort description|Endofunctor on the category V of finite-dimensional vector spaces}} ...of finite-dimensional vector spaces]] that depends polynomially on vector spaces. For example, the [[symmetric power]]s <math>V \mapsto \operatorname{Sym}^n ...

...mposition of ''R'' is a representation of ''R'' as a direct sum (of vector spaces) ...s a homogeneous element and the ''d'' elements ''θ''_''i'' are a homogeneous system of parameters for ''R'' and ...

{{Short description|Homogeneous quotient space of a semisimple Lie group by a parabolic subgroup}} ...metry]] and the study of [[Lie group]]s, a '''parabolic geometry''' is a [[homogeneous space]] ''G''/''P'' which is the quotient of a [[semisimple Lie group]] ''G ...

...grating]] over [[sphere]]s, one integrates over generalized spheres: for a homogeneous space ''X''&nbsp;=&nbsp;''G''/''H'', a '''generalized sphere''' centered at * the dot denotes the action of the group ''G'' on the homogeneous space ''X'' ...

...nspace]]s of ''θ'' are the spaces of [[homogeneous function]]s. ([[Euler's homogeneous function theorem]]) ...

...theorem]], which counts the number of isolated common zeros of a set of [[homogeneous polynomial]]s. This generalization is due to [[Igor Shafarevich]].<ref>{{ci Multi-homogeneous Bézout theorem provides such a better bound when the unknowns may be split ...

...in [[metric space]] that contains all [[separable space|separable]] metric spaces in a particularly nice manner. This [[mathematics]] concept is due to [[Pav ...''Urysohn universal''<ref>{{citation|title=Geometric embeddings of metric spaces|url=http://www.math.jyu.fi/research/reports/rep90.ps|author=Juha Heinonen|d ...

...is a maximal such space, with quotient maps going down to all of the other spaces, that is called the Furstenberg boundary. ...Lizhen|last2=Ji|title=Compactifications of symmetric and locally symmetric spaces|url=http://dept.math.lsa.umich.edu/~lji/head.pdf}} ...

...uan José Torrens (2007), "An extension of a bound for functions in Sobolev spaces, with applications to (m,s)-spline interpolation and smoothing" ''Numerisch ...de Silanes; Juan José Torrens (2009), "Estimates for functions in Sobolev spaces defined on unbounded domains" ''Journal of Approximation Theory'' ...

...</math> of structures; the elements of <math>X_i</math> are said to be "'''homogeneous''' of '''degree''' ''i''{{-"}}. ...|direct sum]] <math display="inline">V = \bigoplus_{i \in I} V_i</math> of spaces. ...

...tract [[algebraic geometry]] and to describe some basic uses of projective spaces. == Homogeneous polynomial ideals== ...

...[[Convex function|convex]] [[Order theory|order theoretic]] views on state spaces of physical systems. .... The cone is called ''self-dual'' when <math>C=C^*</math>. It is called ''homogeneous'' when to any two points <math>a,b \in C</math> there is a real [[linear tr ...

...This vector field is radial in the sense that it vanishes uniformly on 0-homogeneous functions, that is, the functions that are invariant by homothetic rescalin ...o a 0-homogeneous function on ''V'' (again partially defined). We obtain 1-homogeneous vector fields by multiplying the Euler vector field by such functions. This ...

In other words, every additive map is [[Homogeneous function|homogeneous over the integers]]. Consequently, every additive map between [[abelian gro In other words, every additive map is [[homogeneous over the rational numbers]]. Consequently, every additive maps between unit ...

...stablish size and decay of solutions in [[mixed norm]] [[Lp space|Lebesgue spaces]]. They were first noted by [[Robert Strichartz]] and arose out of connect In this case the homogeneous Strichartz estimates take the form:<ref name=tao2006>{{citation|author=Tao, ...

...m cohomology|eprint=alg-geom/9608011|pages=6,12,29,31}}</ref> These moduli spaces are smooth [[orbifold]]s whenever the target space is convex. A variety <ma There are many examples of convex spaces, including the following. ...

...d to be a ''Busemann'' ''G''-''space''. Every Busemann ''G''-space is a [[homogeneous space]]. ...23}}</ref><ref>{{cite book|last1=Papadopoulos|first1=Athanase|title=Metric Spaces, Convexity and Nonpositive Curvature|date=2005|publisher=European Mathemati ...

The fibres are therefore vector spaces, and the projection ''p'' is a [[vector bundle]] over the [[Grassmannian]], As a [[homogeneous space]], the affine Grassmannian of an ''n''-dimensional vector space ''V'' ...

...hat is also homogeneous, and these examples are in fact the only compact homogeneous strictly nearly Kähler 6-manifolds.<ref>{{cite journal| title= Classification of homogeneous nearly Kähler manifolds| ...

Since real oriented Grassmannians can be expressed as a [[homogeneous space]] by: == Simplest classifying spaces == ...