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Arthur Cayley
Arthur Cayley (; 16 August 1821 – 26 January 1895) was a prolific British mathematician who worked mostly on algebra. He helped found the modern British school of pure mathematics. As a child, Cayley enjoyed solving complex maths problems for amusement. He entered Trinity College, Cambridge, where he excelled in Greek, French, German, and Italian, as well as mathematics. He worked as a lawyer for 14 years. He postulated the Cayley–Hamilton theorem—that every square matrix is a root of its own characteristic polynomial, and verified it for matrices of order 2 and 3. He was the first to define the concept of a group in the modern way—as a set with a binary operation satisfying certain laws. Formerly, when mathematicians spoke of "groups", they had meant permutation groups. Cayley tables and Cayley graphs as well as Cayley's theorem are named in honour of Cayley. Early years Arthur Cayley was born in Richmond, London, England, on 16 August 1821. His fathe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Richmond, London
Richmond is a town in south-west London,The London Government Act 1963 (c.33) (as amended) categorises the London Borough of Richmond upon Thames as an Outer London borough. Although it is on both sides of the River Thames, the Boundary Commission for England defines it as being in South London or the South Thames sub-region, pairing it with Kingston upon Thames for the purposes of devising constituencies. However, for the purposes of the London Plan, Richmond now lies within the West London region. west-southwest of Charing Cross. It is on a meander of the River Thames, with many parks and open spaces, including Richmond Park, and many protected conservation areas, which include much of Richmond Hill. A specific Act of Parliament protects the scenic view of the River Thames from Richmond. Richmond was founded following Henry VII's building of Richmond Palace in the 16th century, from which the town derives its name. (The palace itself was named after Henry's earld ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Function
In mathematics, a binary function (also called bivariate function, or function of two variables) is a function that takes two inputs. Precisely stated, a function f is binary if there exists sets X, Y, Z such that :\,f \colon X \times Y \rightarrow Z where X \times Y is the Cartesian product of X and Y. Alternative definitions Set-theoretically, a binary function can be represented as a subset of the Cartesian product X \times Y \times Z, where (x,y,z) belongs to the subset if and only if f(x,y) = z. Conversely, a subset R defines a binary function if and only if for any x \in X and y \in Y, there exists a unique z \in Z such that (x,y,z) belongs to R. f(x,y) is then defined to be this z. Alternatively, a binary function may be interpreted as simply a function from X \times Y to Z. Even when thought of this way, however, one generally writes f(x,y) instead of f((x,y)). (That is, the same pair of parentheses is used to indicate both function application and the formation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Group (mathematics)
In mathematics, a group is a set and an operation that combines any two elements of the set to produce a third element of the set, in such a way that the operation is associative, an identity element exists and every element has an inverse. These three axioms hold for number systems and many other mathematical structures. For example, the integers together with the addition operation form a group. The concept of a group and the axioms that define it were elaborated for handling, in a unified way, essential structural properties of very different mathematical entities such as numbers, geometric shapes and polynomial roots. Because the concept of groups is ubiquitous in numerous areas both within and outside mathematics, some authors consider it as a central organizing principle of contemporary mathematics. In geometry groups arise naturally in the study of symmetries and geometric transformations: The symmetries of an object form a group, called the symmetry group of th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Characteristic Polynomial
In linear algebra, the characteristic polynomial of a square matrix is a polynomial which is invariant under matrix similarity and has the eigenvalues as roots. It has the determinant and the trace of the matrix among its coefficients. The characteristic polynomial of an endomorphism of a finite-dimensional vector space is the characteristic polynomial of the matrix of that endomorphism over any base (that is, the characteristic polynomial does not depend on the choice of a basis). The characteristic equation, also known as the determinantal equation, is the equation obtained by equating the characteristic polynomial to zero. In spectral graph theory, the characteristic polynomial of a graph is the characteristic polynomial of its adjacency matrix. Motivation In linear algebra, eigenvalues and eigenvectors play a fundamental role, since, given a linear transformation, an eigenvector is a vector whose direction is not changed by the transformation, and the correspondin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Square Matrix
In mathematics, a square matrix is a matrix with the same number of rows and columns. An ''n''-by-''n'' matrix is known as a square matrix of order Any two square matrices of the same order can be added and multiplied. Square matrices are often used to represent simple linear transformations, such as shearing or rotation. For example, if R is a square matrix representing a rotation (rotation matrix) and \mathbf is a column vector describing the position of a point in space, the product R\mathbf yields another column vector describing the position of that point after that rotation. If \mathbf is a row vector, the same transformation can be obtained using where R^ is the transpose of Main diagonal The entries a_ (''i'' = 1, …, ''n'') form the main diagonal of a square matrix. They lie on the imaginary line which runs from the top left corner to the bottom right corner of the matrix. For instance, the main diagonal of the 4×4 matrix above contains the elements , , , . ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lawyer
A lawyer is a person who practices law. The role of a lawyer varies greatly across different legal jurisdictions. A lawyer can be classified as an advocate, attorney, barrister, canon lawyer, civil law notary, counsel, counselor, solicitor, legal executive, or public servant — with each role having different functions and privileges. Working as a lawyer generally involves the practical application of abstract legal theories and knowledge to solve specific problems. Some lawyers also work primarily in advancing the interests of the law and legal profession. Terminology Different legal jurisdictions have different requirements in the determination of who is recognized as being a lawyer. As a result, the meaning of the term "lawyer" may vary from place to place. Some jurisdictions have two types of lawyers, barrister and solicitors, while others fuse the two. A barrister (also known as an advocate or counselor in some jurisdictions) is a lawyer who typically specializ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Italian Language
Italian (''italiano'' or ) is a Romance language of the Indo-European language family that evolved from the Vulgar Latin of the Roman Empire. Together with Sardinian, Italian is the least divergent language from Latin. Spoken by about 85 million people (2022), Italian is an official language in Italy, Switzerland ( Ticino and the Grisons), San Marino, and Vatican City. It has an official minority status in western Istria (Croatia and Slovenia). Italian is also spoken by large immigrant and expatriate communities in the Americas and Australia.Ethnologue report for language code:ita (Italy) – Gordon, Raymond G., Jr. (ed.), 2005. Ethnologue: Languages of the World, Fifteenth edition. Dallas, Tex.: SIL International. Online version ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
German Language
German ( ) is a West Germanic language mainly spoken in Central Europe. It is the most widely spoken and official or co-official language in Germany, Austria, Switzerland, Liechtenstein, and the Italian province of South Tyrol. It is also a co-official language of Luxembourg and Belgium, as well as a national language in Namibia. Outside Germany, it is also spoken by German communities in France ( Bas-Rhin), Czech Republic ( North Bohemia), Poland (Upper Silesia), Slovakia ( Bratislava Region), and Hungary (Sopron). German is most similar to other languages within the West Germanic language branch, including Afrikaans, Dutch, English, the Frisian languages, Low German, Luxembourgish, Scots, and Yiddish. It also contains close similarities in vocabulary to some languages in the North Germanic group, such as Danish, Norwegian, and Swedish. German is the second most widely spoken Germanic language after English, which is also a West Germanic language. Germ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
French Language
French ( or ) is a Romance languages, Romance language of the Indo-European languages, Indo-European family. It descended from the Vulgar Latin of the Roman Empire, as did all Romance languages. French evolved from Gallo-Romance, the Latin spoken in Gaul, and more specifically in Northern Gaul. Its closest relatives are the other langues d'oïl—languages historically spoken in northern France and in southern Belgium, which French (Francien) largely supplanted. French was also substratum, influenced by native Celtic languages of Northern Roman Gaul like Gallia Belgica and by the (Germanic languages, Germanic) Frankish language of the post-Roman Franks, Frankish invaders. Today, owing to France's French colonial empire, past overseas expansion, there are numerous French-based creole languages, most notably Haitian Creole language, Haitian Creole. A French-speaking person or nation may be referred to as Francophone in both English and French. French is an official language in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Greek Language
Greek ( el, label= Modern Greek, Ελληνικά, Elliniká, ; grc, Ἑλληνική, Hellēnikḗ) is an independent branch of the Indo-European family of languages, native to Greece, Cyprus, southern Italy ( Calabria and Salento), southern Albania, and other regions of the Balkans, the Black Sea coast, Asia Minor, and the Eastern Mediterranean. It has the longest documented history of any Indo-European language, spanning at least 3,400 years of written records. Its writing system is the Greek alphabet, which has been used for approximately 2,800 years; previously, Greek was recorded in writing systems such as Linear B and the Cypriot syllabary. The alphabet arose from the Phoenician script and was in turn the basis of the Latin, Cyrillic, Armenian, Coptic, Gothic, and many other writing systems. The Greek language holds a very important place in the history of the Western world. Beginning with the epics of Homer, ancient Greek literature includes many works ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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