Suppose is a square matrix. If A is a 1-by-1 matrix, then If A is a 2-by-2 matrix, then For a 3-by-3 matrix A, the formula is more complicated: For a general n-by-n matrix, the determinant was defined by Gottfried Leibniz with wha ...

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Determinant, Determinant - Determinants of 2-by-2 matrices, Determinant - Applications, Determinant - General definition and computation, Determinant - Example, Determinant - Properties, Determinant - Derivative, Determinant - Generalizations and related functions, Determinant - Algorithmic implementation, Determinant - History

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Determinism - Philosophy of determinism Determinism - The nature of determinism
Determinism - Determinism in Western tradition Determinism - Determinism in Eastern tradition
Determinism - Arguments against determinism
Determinism - Argument from morality Determinism - Determinism quantum mechanics and classical physics Determinism - First cause
Determinism - A multi-deterministic position Determinism - Modern perspectives on determinism
Determinism - Scientific determinism and first cause Determinism - Determinism and generative processes

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As was pointed out above, it is possible to unambiguously define the determinant of any linear map f : V → V, if V is a finite-dimensional vector space. It makes sense to define the determinant for matrices whose entries come from any commutative ring. The computation rules, the Leibniz formula and the compatibility with matrix multiplication remain valid, except that now a matrix A is invertible if and only if See also:

Determinant, Determinant - Determinants of 2-by-2 matrices, Determinant - Applications, Determinant - General definition and computation, Determinant - Example, Determinant - Properties, Determinant - Derivative, Determinant - Generalizations and related functions, Determinant - Algorithmic implementation, Determinant - History

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The exact meaning of the term "determinism" has historically been subject to various interpretations. Some view determinism and free will as mutually exclusive, whereas others, labelled "Compatibilists", believe that the two ideas can be coherently reconciled. Most of this disagreement is due to the fact that the definition of "free will," like determinism, varies. Some feel it refers to the metaphysical truth of independent agency, whereas others simply define it as the feeling of agency that humans experience when they act. For example, Da ...

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Determinism, Determinism - Philosophy of determinism, Determinism - The nature of determinism, Determinism - Determinism in Western tradition, Determinism - Determinism in Eastern tradition, Determinism - Arguments against determinism, Determinism - Argument from morality, Determinism - Determinism quantum mechanics and classical physics, Determinism - First cause, Determinism - A multi-deterministic position, Determinism - Modern perspectives on determinism, Determinism - Scientific determinism and first cause, Determinism - Determinism and generative processes

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The exact meaning of the term "determinism" has historically been subject to various interpretations. Some view determinism and free will as mutually exclusive, whereas others, labelled "Compatibilists", believe that the two ideas can be coherently reconciled. Most of this disagreement is due to the fact that the definition of "free will," like determinism, varies. Some feel it refers to the metaphysical truth of independent agency, whereas others simply define it as the feeling of agency that humans experience when they act. For example, Da ...

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Determinism, Determinism - Philosophy of determinism, Determinism - The nature of determinism, Determinism - Determinism in Western tradition, Determinism - Determinism in Eastern tradition, Determinism - A multi-deterministic position, Determinism - Modern perspectives on determinism, Determinism - Scientific determinism and first cause, Determinism - Determinism and generative processes, Determinism - Arguments against determinism, Determinism - Argument from morality, Determinism - Determinism quantum mechanics and classical physics, Determinism - First cause

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Computer-generated imagery (CGI) is the application of the field of computer graphics (or more specifically, 3D computer graphics) to special effects. CGI is used in movies, television programs and commercials, and in printed media. Video games most often use real-time computer graphics (rarely referred to as CGI), but may also include pre-rendered "cut scenes" and intro movies that ...

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Computer-generated imagery - History Computer-generated imagery - Creating characters and objects on a computer Computer-generated imagery - Free CGI Tools Available Online for Download

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A definition may be a statement of the essential properties of a certain thing, or a statement of equivalence between one expression and another, usually more complex expression that gives the meaning of the first. These two senses are not mutually exclusive, nor are they equivalent. A thing being defined is called (from Latin) a definiendum; the expression which defines it is called a definiens. Definition - Kinds of definition. A number of different kinds and techniques of definition ...

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Definition - Kinds of definition Definition - Determining meaning: extension intension ambiguity and vagueness Definition - A definition of 'definition' Definition - A contribution to defining the term 'definition' Definition - Quotation

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Originally, the word computing was synonymous with counting and calculating, and a science that deals with the original sense of computing mathematical calculations. "Computing" has come to mean the operation and usage of computing machines, the electrical processes carried out within the computing hardware itself, and the theoretical concepts governing them (computer science). The following definition of computing is gi ...

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Computing - Science and theory Computing - Hardware
Computing - Instruction-level taxonomies
Computing - Software Computing - History of computing Computing - Business computing Computing - Human factors Computing - Computer security Computing - Data
Computing - Numeric data Computing - Character data Computing - Other data topics
Computing - Mechatronics Computing - Classes of computers Computing - Companies - current Computing - Companies - historic Computing - Professional organizations Computing - Standards organizations and consortia Computing - Miscellaneous

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Determinism - Argument from morality. Some critics of determinism argue that if people are assumed incapable of independent choice (free will) there can then be no rational basis for morality, and therefore some aspects of criminal and civil jurisprudence and legislation appear irrational and unjust. How, they ask, can one be punished for an involuntary action? In order to maintain the integrity of social institutions that rely in part upon holding people responsible for their actions, it becomes necessary in their eyes to deny determinism, at least as fa ...

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Determinism, Determinism - Philosophy of determinism, Determinism - The nature of determinism, Determinism - Determinism in Western tradition, Determinism - Determinism in Eastern tradition, Determinism - Arguments against determinism, Determinism - Argument from morality, Determinism - Determinism quantum mechanics and classical physics, Determinism - First cause, Determinism - A multi-deterministic position, Determinism - Modern perspectives on determinism, Determinism - Scientific determinism and first cause, Determinism - Determinism and generative processes

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In computer science, computability theory is the branch of the theory of computation that studies which problems are computationally solvable using different models of computation. Computability theory differs from the related discipline of computational complexity theory, which deals with the question of how efficiently a problem can be solved, rather than whether it is solvable at all. Computability theory computation - Introduction. A central question of computer science is to address the limits o ...

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Computability theory computation - Introduction Computability theory computation - Formal models of computation Computability theory computation - Power of computational models
Computability theory computation - Power of finite state machines Computability theory computation - Power of push-down automata Computability theory computation - Power of Turing machines
Computability theory computation - Unreasonable models of computation
Computability theory computation - Infinite execution Computability theory computation - Oracle machines Computability theory computation - Limits of hypercomputation
Computability theory computation - History of computability theory

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A sex-determination system is a biological system that determines the development of sexual characteristics in an organism. In many cases, sex determination is genetic: males and females have different alleles or even different genes that specify their sexual morphology. In animals, this is often accompanied by chromosomal differences. In other cases, sex is determined by environmental variables (such as temperature) or social variables (the size of an organism relative to other members of its population). The details of some sex-dete ...

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Sex-determination system - Chromosomal determination
Sex-determination system - Mammals Sex-determination system - Other chromosomal systems
Sex-determination system - Non-genetic sex-determination systems Sex-determination system - Reference

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Put simply, causal determinism expresses the belief that every effect has a cause, and therefore science, pursued diligently enough, will explain all natural phenomena and thus produce a TOE (Theory of Everything). This idea goes hand in hand with materialism. Scientists and skeptics may implicitly favour causal determinism because it does not allow for any supernatural explanations of reality. As Pierre-Simon Laplace noted around 1814, such a theory would also grant a sufficiently powerful being the ability to determine ...

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A computer is a machine capable of processing data according to a program — a list of instructions. The data to be processed may represent many types of information including numbers, text, pictures, or sound. Computers can be extremely versatile. In fact, they are universal information processing machines. According to the Church-Turing thesis, a computer with a certain minimum threshold capability is in principle capable of performing the tasks of any other computer, from those of a personal digital assistant ...

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Computer - History of computing Computer - How computers work: the stored program architecture Computer - Digital circuits
Computer - I/O devices Computer - Programs
Computer - Computer applications
Computer - Networking and the Internet
Computer - Computing professions and disciplines

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Climatic Determinism or Environmental determinism is an aspect of economic geography. Also sometimes called the equatorial paradox. According to this theory, about 70% of the economic development of a country can be predicted from the distance between that country and the equator. In other words, the further from the equator the more developed a country tends to be. The paradox applies equally well both north and south of the equator. Australia, for example, has a higher level of economic development than Indonesia. The paradox also applies within countries - the northern U. ...

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Computer graphics (CG) is the field of visual computing, where one utilizes computers both to generate visual images synthetically and to integrate or alter visual and spatial information sampled from the real world. The first major advance in computer graphics was the development of the Sketchpad in 1962 by Ivan Sutherland. This field can be divided into several areas: real-time 3D rendering (often used in video games), computer animation, video capture and video creation rendering, special effects editing (often ...

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Computer graphics - Computer graphics 2D Computer graphics - Computer graphics 3D Computer graphics - Shading Computer graphics - Texturing Computer graphics - Toolkits and APIs

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Determinism - Argument from morality. Some critics of determinism argue that if people are assumed incapable of independent choice (free will) there can then be no rational basis for morality, and therefore some aspects of criminal and civil jurisprudence and legislation appear irrational and unjust. How, they ask, can one be punished for an involuntary action? In order to maintain the integrity of social institutions that rely in part upon holding people responsible for their actions, it becomes necessary in their eyes to deny determinism, at least as fa ...

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Determinism, Determinism - Philosophy of determinism, Determinism - The nature of determinism, Determinism - Determinism in Western tradition, Determinism - Determinism in Eastern tradition, Determinism - A multi-deterministic position, Determinism - Modern perspectives on determinism, Determinism - Scientific determinism and first cause, Determinism - Determinism and generative processes, Determinism - Arguments against determinism, Determinism - Argument from morality, Determinism - Determinism quantum mechanics and classical physics, Determinism - First cause

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Just as arguments can be good or bad, definitions can be good or bad. A definition gives us the meaning of a word. To understand this more deeply requires an elucidation of a few features of meaning, the principal ones being extension, intension, ambiguity, and vagueness. An ostensive definition points out examples by which one gains a sense of the meaning of a word. An extensional definition exhaustively lists every referent of a word (the completion of an ostensive exploration). An intensional definiti ...

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Definition, Definition - Kinds of definition, Definition - Determining meaning: extension intension ambiguity and vagueness, Definition - A definition of 'definition', Definition - A contribution to defining the term 'definition', Definition - Quotation

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A partial function is called computable if the graph of f is a recursively enumerable set. The set of partial computable functions with one parameter is usually denoted or if the number of parameters is clear from the context. A total function is called computable if the graph of f is a recursive set. The set of total computable fun ...

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Computable function, Computable function - Definition, Computable function - Remarks, Computable function - Examples, Computable function - Properties

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A virus is a type of program that can replicate itself by making (possibly modified) copies of itself. The main criterion for classifying a piece of executable code as a virus is that it spreads itself by means of 'hosts'. A virus can only spread from one computer to another when its host is taken to the uninfected computer, for instance by a user sending it over a network or carrying it on a removable media. Additionally, viruses can spread to other computers by infecting files on a network file system or a file system that is accessed by a ...

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Computer virus, Computer virus - Definition, Computer virus - Use of the word virus, Computer virus - History, Computer virus - Why people create computer viruses, Computer virus - Replication Strategies, Computer virus - Nonresident viruses, Computer virus - Resident viruses, Computer virus - Host types, Computer virus - Methods to avoid detection, Computer virus - Avoiding bait files and other undesirable hosts, Computer virus - Stealth, Computer virus - Self-modification, Computer virus - Viruses and legitimate software, Computer virus - The vulnerability of operating systems to viruses, Computer virus - The role of software development, Computer virus - Anti-virus software and other countermeasures

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A virus is a type of program that can replicate itself by making (possibly modified) copies of itself. The main criterion for classifying a piece of executable code as a virus is that it spreads itself by means of 'hosts'. A virus can only spread from one computer to another when its host is taken to the uninfected computer, for instance by a user sending it over a network or carrying it on a removable medium. Additionally, viruses can spread to other computers by infecting files on a network file system or a file system that is accessed by ...

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Computer virus, Computer virus - Definition, Computer virus - Use of the word virus, Computer virus - History, Computer virus - Why people create computer viruses, Computer virus - Replication Strategies, Computer virus - Nonresident viruses, Computer virus - Resident viruses, Computer virus - Host types, Computer virus - Methods to avoid detection, Computer virus - Avoiding bait files and other undesirable hosts, Computer virus - Stealth, Computer virus - Self-modification, Computer virus - Viruses and legitimate software, Computer virus - The vulnerability of operating systems to viruses, Computer virus - The role of software development, Computer virus - Anti-virus software and other countermeasures

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