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Subspace Lattice
Subspace may refer to: Mathematics * Subspace (mathematics), a particular subset of a parent space * A subset of a topological space endowed with the subspace topology * Linear subspace, in linear algebra, a subset of a vector space that is closed under addition and scalar multiplication * Flat (geometry), a Euclidean subspace * Affine subspace, a geometric structure that generalizes the affine properties of a flat * Projective space#Projective subspace, Projective subspace, a geometric structure that generalizes a linear subspace of a vector space * Multilinear subspace in multilinear algebra, a subset of a tensor space that is closed under addition and scalar multiplication Science fiction * Also known as hyperspace * Subspace (Star Trek), Subspace (''Star Trek''), a fictional feature of space-time that facilitates faster-than-light communication and transit Games * SubSpace (video game), ''SubSpace'' (video game), a two-dimensional space shooter computer game * Super Smash Bro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Subspace (mathematics)
In mathematics, a space is a Set (mathematics), set (sometimes known as a Universe (mathematics), ''universe'') endowed with a mathematical structure, structure defining the relationships among the Element (mathematics), elements of the set. A subspace is a subset of the parent space which retains the same structure. While modern mathematics uses many types of spaces, such as Euclidean spaces, linear spaces, topological spaces, Hilbert spaces, or probability spaces, it does not define the notion of "space" itself. A space consists of selected mathematical objects that are treated as Point (mathematics), points, and selected relationships between these points. The nature of the points can vary widely: for example, the points can represent numbers, functions on another space, or subspaces of another space. It is the relationships that define the nature of the space. More precisely, isomorphic spaces are considered identical, where an isomorphism between two spaces is a one-to-one ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Subspace Topology
In topology and related areas of mathematics, a subspace of a topological space (''X'', ''𝜏'') is a subset ''S'' of ''X'' which is equipped with a topology induced from that of ''𝜏'' called the subspace topology (or the relative topology, or the induced topology, or the trace topology).; see Section 26.2.4. Submanifolds, p. 59 Definition Given a topological space (X, \tau) and a subset S of X, the subspace topology on S is defined by :\tau_S = \lbrace S \cap U \mid U \in \tau \rbrace. That is, a subset of S is open in the subspace topology if and only if it is the intersection of S with an open set in (X, \tau). If S is equipped with the subspace topology then it is a topological space in its own right, and is called a subspace of (X, \tau). Subsets of topological spaces are usually assumed to be equipped with the subspace topology unless otherwise stated. Alternatively we can define the subspace topology for a subset S of X as the coarsest topology for which the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Subspace
In mathematics, the term ''linear'' is used in two distinct senses for two different properties: * linearity of a ''function (mathematics), function'' (or ''mapping (mathematics), mapping''); * linearity of a ''polynomial''. An example of a linear function is the function defined by f(x)=(ax,bx) that maps the real line to a line in the Euclidean plane R2 that passes through the origin. An example of a linear polynomial in the variables X, Y and Z is aX+bY+cZ+d. Linearity of a mapping is closely related to ''Proportionality (mathematics), proportionality''. Examples in physics include the linear relationship of voltage and Electric current, current in an electrical conductor (Ohm's law), and the relationship of mass and weight. By contrast, more complicated relationships, such as between velocity and kinetic energy, are ''Nonlinear system, nonlinear''. Generalized for functions in more than one dimension (mathematics), dimension, linearity means the property of a function of b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Flat (geometry)
In geometry, a flat is an affine subspace, i.e. a subset of an affine space that is itself an affine space. Particularly, in the case the parent space is Euclidean, a flat is a Euclidean subspace which inherits the notion of distance from its parent space. In an -dimensional space, there are -flats of every dimension from 0 to ; flats one dimension lower than the parent space, -flats, are called '' hyperplanes''. The flats in a plane (two-dimensional space) are points, lines, and the plane itself; the flats in three-dimensional space are points, lines, planes, and the space itself. The definition of flat excludes non-straight curves and non-planar surfaces, which are subspaces having different notions of distance: arc length and geodesic length, respectively. Flats occur in linear algebra, as geometric realizations of solution sets of systems of linear equations. A flat is a manifold and an algebraic variety, and is sometimes called a ''linear manifold'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Affine Subspace
In mathematics, an affine space is a geometry, geometric structure (mathematics), structure that generalizes some of the properties of Euclidean spaces in such a way that these are independent of the concepts of distance (mathematics), distance and measure of angles, keeping only the properties related to parallel (geometry), parallelism and ratio of lengths for parallel line segments. Affine space is the setting for affine geometry. As in Euclidean space, the fundamental objects in an affine space are called ''point (geometry), points'', which can be thought of as locations in the space without any size or shape: zero-dimensional. Through any pair of points an infinite straight line can be drawn, a one-dimensional set of points; through any three points that are not collinear, a two-dimensional plane (geometry), plane can be drawn; and, in general, through points in general position, a -dimensional flat (geometry), flat or affine subspace can be drawn. Affine space is charact ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Projective Space
In mathematics, the concept of a projective space originated from the visual effect of perspective, where parallel lines seem to meet ''at infinity''. A projective space may thus be viewed as the extension of a Euclidean space, or, more generally, an affine space with points at infinity, in such a way that there is one point at infinity of each direction of parallel lines. This definition of a projective space has the disadvantage of not being isotropic, having two different sorts of points, which must be considered separately in proofs. Therefore, other definitions are generally preferred. There are two classes of definitions. In synthetic geometry, ''point'' and ''line'' are primitive entities that are related by the incidence relation "a point is on a line" or "a line passes through a point", which is subject to the axioms of projective geometry. For some such set of axioms, the projective spaces that are defined have been shown to be equivalent to those resulting from the f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multilinear Subspace
Multilinear subspace learning is an approach for disentangling the causal factor of data formation and performing dimensionality reduction.M. A. O. Vasilescu, D. Terzopoulos (2003"Multilinear Subspace Analysis of Image Ensembles" "Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR’03), Madison, WI, June, 2003"M. A. O. Vasilescu, D. Terzopoulos (2002"Multilinear Analysis of Image Ensembles: TensorFaces" Proc. 7th European Conference on Computer Vision (ECCV'02), Copenhagen, Denmark, May, 2002M. A. O. Vasilescu,(2002"Human Motion Signatures: Analysis, Synthesis, Recognition" "Proceedings of International Conference on Pattern Recognition (ICPR 2002), Vol. 3, Quebec City, Canada, Aug, 2002, 456–460." The Dimensionality reduction can be performed on a data tensor that contains a collection of observations that have been vectorized, or observations that are treated as matrices and concatenated into a data tensor.X. He, D. Cai, P. NiyogiTensor su ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hyperspace
In science fiction, hyperspace (also known as nulspace, subspace, overspace, jumpspace and similar terms) is a concept relating to higher dimensions as well as parallel universes and a faster-than-light (FTL) method of interstellar travel. In its original meaning, the term ''hyperspace'' was simply a synonym for higher-dimensional space. This usage was most common in 19th-century textbooks and is still occasionally found in academic and popular science texts, for example, '' Hyperspace'' (1994).'''' Its science fiction usage originated in the magazine '' Amazing Stories Quarterly'' in 1931 and within several decades it became one of the most popular tropes of science fiction, popularized by its use in the works of authors such as Isaac Asimov and E. C. Tubb, and media franchises such as ''Star Wars''. One of the main reasons for the concept's popularity in science fiction is the impossibility of faster-than-light travel in ordinary '' physical space'', which hyperspace ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Subspace (Star Trek)
The fictional technology in ''Star Trek'' has borrowed many ideas from the scientific world. Episodes often contain technologies named after or inspired by real-world scientific concepts, such as tachyon beams, baryon sweeps, quantum Slipstream (science fiction), slipstream drives, and photon Weapons in Star Trek, torpedoes. Some of the technologies created for the ''Star Trek'' universe were done so out of financial necessity. For instance, the transporter (Star Trek), transporter was created because the limited budget of ''Star Trek: The Original Series'' (''TOS'') in the 1960s did not allow expensive shots of spaceships landing on planets. ''Discovery Channel Magazine'' stated that cloaking devices, faster-than-light travel, and transporter (Star Trek), dematerialized transport were only dreams at the time ''TOS'' was made, but physicist Michio Kaku believes all these things are possible. William Shatner, who portrayed James T. Kirk in ''TOS'', believes this as well, and wen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SubSpace (video Game)
''SubSpace'' is a 2D space shooter video game created in 1995 and released in 1997 by Virgin Interactive which was a finalist for the Academy of Interactive Arts & Sciences Online Game of the Year Award in 1998. ''SubSpace'' incorporates quasi-realistic zero-friction physics into a massively multiplayer online game. The game is no longer operated by VIE; instead, fans and players of the game provide servers and technical updates. The action is viewed from above, which presents challenges very different from those of a three-dimensional game. The game has no built-in story or set of goals; players may enter a variety of servers, each of which have differing objectives, maps, sounds, and graphics. ''SubSpace'' is considered an early entry in the massively multiplayer online genre due to its unprecedented player counts. History ''SubSpace'' evolved from a game originally called ''Sniper'' (1995), a project to test the effects and severity of lag in a massively multiplayer en ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Subspace Emissary
''Super Smash Bros. Brawl'' is a 2008 crossover fighting game developed by Sora Ltd. and published by Nintendo for the Wii. The third installment in the ''Super Smash Bros.'' series and the successor to '' Super Smash Bros. Melee'', it was the first game in the series not to be developed primarily by HAL Laboratory. It was developed by a creative team under Sora that included members from several Nintendo and third-party development teams. It was announced at a pre- E3 2005 press conference by Nintendo president Satoru Iwata. Masahiro Sakurai, director of the previous two games in the series, assumed the role of director at Iwata's request. Game development began in October 2005; after delays due to development problems, the game was released worldwide in 2008. The number of playable characters in ''Brawl'' has grown from that in ''Super Smash Bros. Melee'', although some characters from ''Melee'' were cut in the game. ''Brawl'' is the first game in the series to have playa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Subspace (song)
Subspace may refer to: Mathematics * Subspace (mathematics), a particular subset of a parent space * A subset of a topological space endowed with the subspace topology * Linear subspace, in linear algebra, a subset of a vector space that is closed under addition and scalar multiplication * Flat (geometry), a Euclidean subspace * Affine subspace, a geometric structure that generalizes the affine properties of a flat * Projective subspace, a geometric structure that generalizes a linear subspace of a vector space * Multilinear subspace in multilinear algebra, a subset of a tensor space that is closed under addition and scalar multiplication Science fiction * Also known as hyperspace In science fiction, hyperspace (also known as nulspace, subspace, overspace, jumpspace and similar terms) is a concept relating to higher dimensions as well as parallel universes and a faster-than-light (FTL) method of interstellar travel ... * Subspace (''Star Trek''), a fictional feature o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
