Linear algebraLinear algebra is the branch of mathematics concerning linear equations such as: linear maps such as: and their representations in vector spaces and through matrices. Linear algebra is central to almost all areas of mathematics. For instance, linear algebra is fundamental in modern presentations of geometry, including for defining basic objects such as lines, planes and rotations. Also, functional analysis, a branch of mathematical analysis, may be viewed as the application of linear algebra to spaces of functions.
Linear mapIn mathematics, and more specifically in linear algebra, a linear map (also called a linear mapping, linear transformation, vector space homomorphism, or in some contexts linear function) is a mapping between two vector spaces that preserves the operations of vector addition and scalar multiplication. The same names and the same definition are also used for the more general case of modules over a ring; see Module homomorphism. If a linear map is a bijection then it is called a .
Linear combinationIn mathematics, a linear combination is an expression constructed from a set of terms by multiplying each term by a constant and adding the results (e.g. a linear combination of x and y would be any expression of the form ax + by, where a and b are constants). The concept of linear combinations is central to linear algebra and related fields of mathematics. Most of this article deals with linear combinations in the context of a vector space over a field, with some generalizations given at the end of the article.
Athlon 64 X2The Athlon 64 X2 is the first native dual-core desktop central processing unit (CPU) designed by Advanced Micro Devices (AMD). It was designed from scratch as native dual-core by using an already multi-CPU enabled Athlon 64, joining it with another functional core on one die, and connecting both via a shared dual-channel memory controller/north bridge and additional control logic. The initial versions are based on the E stepping model of the Athlon 64 and, depending on the model, have either 512 or 1024 KB of L2 cache per core.
Linear regressionIn statistics, linear regression is a linear approach for modelling the relationship between a scalar response and one or more explanatory variables (also known as dependent and independent variables). The case of one explanatory variable is called simple linear regression; for more than one, the process is called multiple linear regression. This term is distinct from multivariate linear regression, where multiple correlated dependent variables are predicted, rather than a single scalar variable.
General linear modelThe general linear model or general multivariate regression model is a compact way of simultaneously writing several multiple linear regression models. In that sense it is not a separate statistical linear model. The various multiple linear regression models may be compactly written as where Y is a matrix with series of multivariate measurements (each column being a set of measurements on one of the dependent variables), X is a matrix of observations on independent variables that might be a design matrix (each column being a set of observations on one of the independent variables), B is a matrix containing parameters that are usually to be estimated and U is a matrix containing errors (noise).
Id Techid Tech is a series of separate game engines designed and developed by id Software. Prior to the presentation of the id Tech 5-based game Rage in 2011, the engines lacked official designation and as such were simply referred to as the Doom and Quake engines, from the name of the main game series the engines had been developed for. "id Tech" has been released as free software under the GNU General Public License. id Tech versions 0 to 3 were released under GPL-2.0-or-later. id Tech versions 3.5 to 4.
Linear programmingLinear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. Linear programming is a special case of mathematical programming (also known as mathematical optimization). More formally, linear programming is a technique for the optimization of a linear objective function, subject to linear equality and linear inequality constraints.
Exterior algebraIn mathematics, the exterior algebra, or Grassmann algebra, named after Hermann Grassmann, is an algebra that uses the exterior product or wedge product as its multiplication. In mathematics, the exterior product or wedge product of vectors is an algebraic construction used in geometry to study areas, volumes, and their higher-dimensional analogues. The exterior product of two vectors and , denoted by is called a bivector and lives in a space called the exterior square, a vector space that is distinct from the original space of vectors.
Vector spaceIn mathematics and physics, a vector space (also called a linear space) is a set whose elements, often called vectors, may be added together and multiplied ("scaled") by numbers called scalars. Scalars are often real numbers, but can be complex numbers or, more generally, elements of any field. The operations of vector addition and scalar multiplication must satisfy certain requirements, called vector axioms. The terms real vector space and complex vector space are often used to specify the nature of the scalars: real coordinate space or complex coordinate space.
Intimate relationshipAn intimate relationship is an interpersonal relationship that involves physical or emotional intimacy. Although an intimate relationship is commonly a sexual relationship, it may also be a non-sexual relationship involving family or friends. Emotional intimacy is an essential aspect of a healthy . Feelings of liking or loving may prompt physical intimacy. However, emotional intimacy may or may not be present alongside physical intimacy depending on the relationship.
GeneralizationA generalization is a form of abstraction whereby common properties of specific instances are formulated as general concepts or claims. Generalizations posit the existence of a domain or set of elements, as well as one or more common characteristics shared by those elements (thus creating a conceptual model). As such, they are the essential basis of all valid deductive inferences (particularly in logic, mathematics and science), where the process of verification is necessary to determine whether a generalization holds true for any given situation.
Legal caseA legal case is in a general sense a dispute between opposing parties which may be resolved by a court, or by some equivalent legal process. A legal case is typically based on either civil or criminal law. In most legal cases, there are one or more accusers and one or more defendants. In some instances, a legal case may occur between parties that are not in opposition, but require a legal ruling to formally establish some legal fact, such as a divorce.
Id Tech 4id Tech 4, popularly known as the Doom 3 engine, is a game engine developed by id Software and first used in the video game Doom 3. The engine was designed by John Carmack, who also created previous game engines, such as those for Doom and Quake, which are widely recognized as significant advances in the field. This OpenGL-based game engine has also been used in Quake 4, Prey, Enemy Territory: Quake Wars, Wolfenstein, and Brink. id Tech 4 is licensed under the terms of the GNU General Public License v3.
Id Softwareid Software LLC (ɪd) is an American video game developer based in Richardson, Texas. It was founded on February 1, 1991, by four members of the computer company Softdisk: programmers John Carmack and John Romero, game designer Tom Hall, and artist Adrian Carmack. id Software made important technological developments in video game technologies for the PC (running MS-DOS and Windows), including work done for the Wolfenstein, Doom, and Quake franchises at the time.
Orientation (vector space)The orientation of a real vector space or simply orientation of a vector space is the arbitrary choice of which ordered bases are "positively" oriented and which are "negatively" oriented. In the three-dimensional Euclidean space, right-handed bases are typically declared to be positively oriented, but the choice is arbitrary, as they may also be assigned a negative orientation. A vector space with an orientation selected is called an oriented vector space, while one not having an orientation selected, is called .
Euclidean vectorIn mathematics, physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector or spatial vector) is a geometric object that has magnitude (or length) and direction. Vectors can be added to other vectors according to vector algebra. A Euclidean vector is frequently represented by a directed line segment, or graphically as an arrow connecting an initial point A with a terminal point B, and denoted by . A vector is what is needed to "carry" the point A to the point B; the Latin word vector means "carrier".
Visual Basic (.NET)Visual Basic (VB), originally called Visual Basic .NET (VB.NET), is a multi-paradigm, object-oriented programming language, implemented on .NET, Mono, and the .NET Framework. Microsoft launched VB.NET in 2002 as the successor to its original Visual Basic language, the last version of which was Visual Basic 6.0. Although the ".NET" portion of the name was dropped in 2005, this article uses "Visual Basic [.NET]" to refer to all Visual Basic languages released since 2002, in order to distinguish between them and the classic Visual Basic.
QuestionA question is an utterance which serves as a request for information. Questions are sometimes distinguished from interrogatives, which are the grammatical forms typically used to express them. Rhetorical questions, for instance, are interrogative in form but may not be considered bona fide questions, as they are not expected to be answered. Questions come in a number of varieties. Polar questions are those such as the English example "Is this a polar question?", which can be answered with "yes" or "no".
Id Tech 3id Tech 3, popularly known as the Quake III Arena engine''', is a game engine developed by id Software for their video game Quake III Arena. It has been adopted by numerous games. During its time, it competed with the Unreal Engine; both engines were widely licensed. While id Tech 3 is based on id Tech 2 engine, a large amount of the code was rewritten. Successor id Tech 4 was derived from id Tech 3, as was Infinity Ward's IW engine used in Call of Duty 2 onwards.
