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Canonical Form
In mathematics and computer science, a canonical, normal, or standard form of a mathematical object is a standard way of presenting that object as a mathematical expression. Often, it is one which provides the simplest representation of an object and allows it to be identified in a unique way. The distinction between "canonical" and "normal" forms varies from subfield to subfield. In most fields, a canonical form specifies a ''unique'' representation for every object, while a normal form simply specifies its form, without the requirement of uniqueness. The canonical form of a positive integer in decimal representation is a finite sequence of digits that does not begin with zero. More generally, for a class of objects on which an equivalence relation is defined, a canonical form consists in the choice of a specific object in each class. For example: *Jordan normal form is a canonical form for matrix similarity. *The row echelon form is a canonical form, when one considers as equ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Anagram Canonical Svg
An anagram is a word or phrase formed by rearranging the letters of a different word or phrase, typically using all the original letters exactly once. For example, the word ''anagram'' itself can be rearranged into the phrase "nag a ram"; which is an Easter egg suggestion in Google after searching for the word "anagram". The original word or phrase is known as the ''subject'' of the anagram. Any word or phrase that exactly reproduces the letters in another order is an anagram. Someone who creates anagrams may be called an "anagrammatist", and the goal of a serious or skilled anagrammatist is to produce anagrams that reflect or comment on their subject. Examples Anagrams may be created as a commentary on the subject. They may be a parody, a criticism or satire. For example: * "The New York Times, New York Times" = "monkeys write" * "Church of Scientology" = "rich-chosen goofy cult" * "McDonald's restaurants" = "Uncle Sam's standard rot" An anagram may also be a synonym of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Idempotence
Idempotence (, ) is the property of certain operations in mathematics and computer science whereby they can be applied multiple times without changing the result beyond the initial application. The concept of idempotence arises in a number of places in abstract algebra (in particular, in the theory of projectors and closure operators) and functional programming (in which it is connected to the property of referential transparency). The term was introduced by American mathematician Benjamin Peirce in 1870 in the context of elements of algebras that remain invariant when raised to a positive integer power, and literally means "(the quality of having) the same power", from + '' potence'' (same + power). Definition An element x of a set S equipped with a binary operator \cdot is said to be ''idempotent'' under \cdot if : . The ''binary operation'' \cdot is said to be ''idempotent'' if : . Examples * In the monoid (\mathbb, \times) of the natural numbers with multiplication, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Friedrich Julius Richelot
Friedrich Julius Richelot (6 November 1808 – 31 March 1875) was a German mathematician, born in Königsberg. He was a student of Carl Gustav Jacob Jacobi. He was promoted in 1831 at the Philosophical Faculty of the University of Königsberg with a dissertation on the division of the circle into 257 equal parts (see references) and was a professor there. Richelot authored numerous publications in German, French and Latin, among them — with his 1832 dissertation — the first known guide to the Euclidean construction of the regular 257-gon with compass and straightedge In geometry, straightedge-and-compass construction – also known as ruler-and-compass construction, Euclidean construction, or classical construction – is the construction of lengths, angles, and other geometric figures using only an Idealiz .... In 1825, he joined the Corps Masovia.Kösener Korps-Listen 1910, 141, 8 He died in Königsberg in 1875. See also * Timeline of abelian varieties References ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gotthold Eisenstein
Ferdinand Gotthold Max Eisenstein (16 April 1823 – 11 October 1852) was a German mathematician who made significant contributions to number theory and mathematical analysis, analysis. Born in Berlin, Prussia, to Jewish parents who converted to Protestantism before his birth, Eisenstein displayed exceptional mathematical talent from a young age. Early life and education Despite suffering from health problems, including meningitis, Eisenstein excelled academically. At 14, he attended Friedrich Werder Gymnasium (school), Gymnasium. By age 15, he had mastered the mathematics curriculum. His teachers recognized his mathematical abilities, one quoted as saying: He then turned to the works of Leonhard Euler and Joseph-Louis Lagrange to study differential calculus. While still a student, Eisenstein began attending lectures by Peter Gustav Lejeune Dirichlet and others at the University of Berlin. In 1843, he met William Rowan Hamilton in Dublin, who introduced him to Niels Henrik A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
James Logan (statesman)
James Logan (20 October 167431 October 1751) was a Scotch-Irish Americans, Scots-Irish Thirteen Colonies, colonial American statesman, administrator, and scholar who served as the fourteenth mayor of Philadelphia and held a number of other public offices. Logan was born in the town of Lurgan in County Armagh, Kingdom of Ireland, Ireland to Ulster Scots people, Ulster Scots Quakers. He served as colonial secretary to William Penn. He was a founding trustee of the Academy and College of Philadelphia, College of Philadelphia, the predecessor of the University of Pennsylvania. Early life Logan was born in Lurgan, County Armagh in present-day Northern Ireland, on 20 October 1674, to parents Patrick Logan (1640–1700) and Isabella, Lady Hume (1647–1722), who married in early 1671, in Midlothian, Scotland. His father had a Master of Arts degree from the University of Edinburgh, and originally was an Anglican clergyman before converting to Quakers, Quakerism. James Logan apprentice ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Archetypal
The concept of an archetype ( ) appears in areas relating to behavior, History of psychology#Emergence of German experimental psychology, historical psychology, philosophy and literary analysis. An archetype can be any of the following: # a statement, pattern of behavior, prototype, "first" form, or a main model that other statements, patterns of behavior, and objects copy, emulate, or "merge" into. Informal synonyms frequently used for this definition include "standard example", "basic example", and the longer-form "archetypal example"; mathematical archetypes often appear as "wikt:canonical, canonical examples". # the Jungian psychology concept of an inherited unconscious predisposition, behavioral trait or tendency ("instinct") shared among the members of the species; as any behavioral trait the tendency comes to being by way of patterns of thought, images, affects or pulsions characterized by its qualitative likeness to distinct narrative constructs; unlike personality traits, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Standard
Standard may refer to: Symbols * Colours, standards and guidons, kinds of military signs * Standard (emblem), a type of a large symbol or emblem used for identification Norms, conventions or requirements * Standard (metrology), an object that bears a defined relationship to a unit of measure used for calibration of measuring devices * Standard (timber unit), an obsolete measure of timber used in trade * Breed standard (also called bench standard), in animal fancy and animal husbandry * BioCompute Standard, a standard for next generation sequencing * ''De facto'' standard, product or system with market dominance * Gold standard, a monetary system based on gold; also used metaphorically for the best of several options, against which the others are measured * Internet Standard, a specification ratified as an open standard by the Internet Engineering Task Force * Learning standards, standards applied to education content * Standard displacement, a naval term describing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Norm
Norm, the Norm or NORM may refer to: In academic disciplines * Normativity, phenomenon of designating things as good or bad * Norm (geology), an estimate of the idealised mineral content of a rock * Norm (philosophy), a standard in normative ethics that is prescriptive rather than a descriptive or explanatory abstraction * Social norm, shared standards of acceptable behavior by groups * Basic norm, a jurisprudence concept by Kelsen * Peremptory norm, a fundamental principle of international law * Norm (artificial intelligence), a set of statements used to regulate artificial intelligence software * Norm, a statistical concept in psychometrics representing the aggregate responses of a standardized and representative group * NORM, naturally occurring radioactive materials * NORM (non-mobile older rural males), an acronym in dialect studies coined by Chambers and Trudgill (1980) for a group to which speakers frequently refer In mathematics * Norm (mathematics), a map that ass ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ancient Greek
Ancient Greek (, ; ) includes the forms of the Greek language used in ancient Greece and the classical antiquity, ancient world from around 1500 BC to 300 BC. It is often roughly divided into the following periods: Mycenaean Greek (), Greek Dark Ages, Dark Ages (), the Archaic Greece, Archaic or Homeric Greek, Homeric period (), and the Classical Greece, Classical period (). Ancient Greek was the language of Homer and of fifth-century Athens, fifth-century Athenian historians, playwrights, and Ancient Greek philosophy, philosophers. It has contributed many words to English vocabulary and has been a standard subject of study in educational institutions of the Western world since the Renaissance. This article primarily contains information about the Homeric Greek, Epic and Classical periods of the language, which are the best-attested periods and considered most typical of Ancient Greek. From the Hellenistic period (), Ancient Greek was followed by Koine Greek, which is regar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Canonical
The adjective canonical is applied in many contexts to mean 'according to the canon' the standard, rule or primary source that is accepted as authoritative for the body of knowledge or literature in that context. In mathematics, ''canonical example'' is often used to mean 'archetype'. Science and technology * Canonical form, a natural unique representation of an object, or a preferred notation for some object Mathematics * * Canonical coordinates, sets of coordinates that can be used to describe a physical system at any given point in time * Canonical map, a morphism that is uniquely defined by its main property * Canonical polyhedron, a polyhedron whose edges are all tangent to a common sphere, whose center is the average of its vertices * Canonical ring, a graded ring associated to an algebraic variety * Canonical injection, in set theory * Canonical representative, in set theory a standard member of each element of a set partition Differential geometry * Canonical one-f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
