Halfspace
Half-space may refer to: * Half-space (geometry), either of the two parts into which a plane divides Euclidean space ** (Poincaré) Half-space model, a model of hyperbolic geometry using a Euclidean half-space ** Siegel upper half-space In mathematics, the Siegel upper half-space of degree ''g'' (or genus ''g'') (also called the Siegel upper half-plane) is the set of ''g'' × ''g'' symmetric matrices over the complex numbers whose imaginary part is positive definite. It ..., a set of complex matrices with positive definite imaginary part * Half-space (punctuation), a spacing character half the width of a regular space * Half-space model (oceanography), an estimate for seabed height in areas without significant subduction {{disambig ...
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Half-space (geometry)
In geometry, a half-space is either of the two parts into which a plane divides the three-dimensional Euclidean space. If the space is two-dimensional, then a half-space is called a ''half-plane'' (open or closed). A half-space in a one-dimensional space is called a ''half-line'' or ray''.'' More generally, a half-space is either of the two parts into which a hyperplane divides an n-dimensional space. That is, the points that are not incident to the hyperplane are partitioned into two convex sets (i.e., half-spaces), such that any subspace connecting a point in one set to a point in the other must intersect the hyperplane. A half-space can be either ''open'' or ''closed''. An open half-space is either of the two open sets produced by the subtraction of a hyperplane from the affine space. A closed half-space is the union of an open half-space and the hyperplane that defines it. The open (closed) ''upper half-space'' is the half-space of all (''x''1, ''x''2, ..., ''x''''n'') suc ...
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Half-space Model
Half-space may refer to: * Half-space (geometry), either of the two parts into which a plane divides Euclidean space ** (Poincaré) Half-space model, a model of hyperbolic geometry using a Euclidean half-space ** Siegel upper half-space, a set of complex matrices with positive definite imaginary part * Half-space (punctuation), a spacing character half the width of a regular space * Half-space model (oceanography) Seafloor spreading, or seafloor spread, is a process that occurs at mid-ocean ridges, where new oceanic crust is formed through volcanic activity and then gradually moves away from the ridge. History of study Earlier theories by Alfred Wegener ...

Siegel Upper Half-space
In mathematics, the Siegel upper half-space of degree ''g'' (or genus ''g'') (also called the Siegel upper half-plane) is the set of ''g'' × ''g'' symmetric matrices over the complex numbers whose imaginary part is positive definite. It was introduced by . It is the symmetric space associated to the symplectic group . The Siegel upper half-space has properties as a complex manifold that generalize the properties of the upper half-plane, which is the Siegel upper half-space in the special case ''g'' = 1. The group of automorphisms preserving the complex structure of the manifold is isomorphic to the symplectic group . Just as the two-dimensional hyperbolic metric is the unique (up to scaling) metric on the upper half-plane whose isometry group is the complex automorphism group = , the Siegel upper half-space has only one metric up to scaling whose isometry group is . Writing a generic matrix ''Z'' in the Siegel upper half-space in terms of its real and imaginary parts a ...
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Half-space (punctuation)
A whitespace character is a character data element that represents white space when text is rendered for display by a computer. For example, a ''space'' character (, ASCII 32) represents blank space such as a word divider in a Western script. A printable character results in output when rendered, but a whitespace character does not. Instead, whitespace characters define the layout of text to a limited degree, interrupting the normal sequence of rendering characters next to each other. The output of subsequent characters is typically shifted to the right (or to the left for right-to-left script) or to the start of the next line. The effect of multiple sequential whitespace characters is cumulative such that the next printable character is rendered at a location based on the accumulated effect of preceding whitespace characters. The origin of the term ''whitespace'' is rooted in the common practice of rendering text on white paper. Normally, a whitespace character is ''not'' ...
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