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Archibald Read Richardson
Archibald Read Richardson FRS (21 August 1881 – 4 November 1954) was a British mathematician known for his work in algebra. Career Richardson collaborated with Dudley E. Littlewood on invariants and group representation theory. They introduced the immanant of a matrix, studied Schur functions and developed the Littlewood–Richardson rule for their multiplication. Awards and honours Richardson was elected a Fellow of the Royal Society Fellowship of the Royal Society (FRS, ForMemRS and HonFRS) is an award granted by the judges of the Royal Society of London to individuals who have made a "substantial contribution to the improvement of natural knowledge, including mathemat ... on 21 March 1946. See also * Quasideterminant References 1881 births 1954 deaths 20th-century British mathematicians Algebraists Fellows of the Royal Society {{UK-mathematician-stub ... [...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] |
Littlewood–Richardson Rule
In mathematics, the Littlewood–Richardson rule is a combinatorial description of the coefficients that arise when decomposing a product of two Schur functions as a linear combination of other Schur functions. These coefficients are natural numbers, which the Littlewood–Richardson rule describes as counting certain skew tableaux. They occur in many other mathematical contexts, for instance as multiplicity in the decomposition of tensor products of finite-dimensional representations of general linear groups, or in the decomposition of certain induced representations in the representation theory of the symmetric group, or in the area of algebraic combinatorics dealing with Young tableaux and symmetric polynomials. Littlewood–Richardson coefficients depend on three partitions, say \lambda,\mu,\nu, of which \lambda and \mu describe the Schur functions being multiplied, and \nu gives the Schur function of which this is the coefficient in the linear combination; in other words ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fellow Of The Royal Society
Fellowship of the Royal Society (FRS, ForMemRS and HonFRS) is an award granted by the judges of the Royal Society of London to individuals who have made a "substantial contribution to the improvement of natural knowledge, including mathematics, engineering science, and medical science". Fellowship of the Society, the oldest known scientific academy in continuous existence, is a significant honour. It has been awarded to many eminent scientists throughout history, including Isaac Newton (1672), Michael Faraday (1824), Charles Darwin (1839), Ernest Rutherford (1903), Srinivasa Ramanujan (1918), Albert Einstein (1921), Paul Dirac (1930), Winston Churchill (1941), Subrahmanyan Chandrasekhar (1944), Dorothy Hodgkin (1947), Alan Turing (1951), Lise Meitner (1955) and Francis Crick (1959). More recently, fellowship has been awarded to Stephen Hawking (1974), David Attenborough (1983), Tim Hunt (1991), Elizabeth Blackburn (1992), Tim Berners-Lee (2001), Venki Ramakrishn ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Biographical Memoirs Of Fellows Of The Royal Society
The ''Biographical Memoirs of Fellows of the Royal Society'' is an academic journal on the history of science published annually by the Royal Society. It publishes obituaries of Fellows of the Royal Society. It was established in 1932 as ''Obituary Notices of Fellows of the Royal Society'' and obtained its current title in 1955, with volume numbering restarting at 1. Prior to 1932, obituaries were published in the ''Proceedings of the Royal Society''. The memoirs are a significant historical record and most include a full bibliography of works by the subjects. The memoirs are often written by a scientist of the next generation, often one of the subject's own former students, or a close colleague. In many cases the author is also a Fellow. Notable biographies published in this journal include Albert Einstein, Alan Turing, Bertrand Russell, Claude Shannon, Clement Attlee, Ernst Mayr, and Erwin Schrödinger. Each year around 40 to 50 memoirs of deceased Fellows of the Royal Society ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Royal Society
The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, recognising excellence in science, supporting outstanding science, providing scientific advice for policy, education and public engagement and fostering international and global co-operation. Founded on 28 November 1660, it was granted a royal charter by King Charles II as The Royal Society and is the oldest continuously existing scientific academy in the world. The society is governed by its Council, which is chaired by the Society's President, according to a set of statutes and standing orders. The members of Council and the President are elected from and by its Fellows, the basic members of the society, who are themselves elected by existing Fellows. , there are about 1,700 fellows, allowed to use the postnominal title FRS (Fellow of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History One of the earliest known mathematicians were Thales of Miletus (c. 624–c.546 BC); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman mathematician recorded by history was Hyp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebra
Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics. Elementary algebra deals with the manipulation of variables (commonly represented by Roman letters) as if they were numbers and is therefore essential in all applications of mathematics. Abstract algebra is the name given, mostly in education, to the study of algebraic structures such as groups, rings, and fields (the term is no more in common use outside educational context). Linear algebra, which deals with linear equations and linear mappings, is used for modern presentations of geometry, and has many practical applications (in weather forecasting, for example). There are many areas of mathematics that belong to algebra, some having "algebra" in their name, such as commutative algebra, and some not, such as Galois theory. The word ''alge ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dudley E
Dudley is a large market town and administrative centre in the county of West Midlands, England, southeast of Wolverhampton and northwest of Birmingham. Historically an exclave of Worcestershire, the town is the administrative centre of the Metropolitan Borough of Dudley; in 2011 it had a population of 79,379. The Metropolitan Borough, which includes the towns of Stourbridge and Halesowen, had a population of 312,900. In 2014 the borough council named Dudley as the capital of the Black Country. Originally a market town, Dudley was one of the birthplaces of the Industrial Revolution and grew into an industrial centre in the 19th century with its iron, coal, and limestone industries before their decline and the relocation of its commercial centre to the nearby Merry Hill Shopping Centre in the 1980s. Tourist attractions include Dudley Zoo and Castle, the 12th century priory ruins, and the Black Country Living Museum. History Early history Dudley has a history dating bac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Immanant Of A Matrix
In mathematics, the immanant of a matrix was defined by Dudley E. Littlewood and Archibald Read Richardson as a generalisation of the concepts of determinant and permanent. Let \lambda=(\lambda_1,\lambda_2,\ldots) be a partition of an integer n and let \chi_\lambda be the corresponding irreducible representation-theoretic character of the symmetric group S_n. The ''immanant'' of an n\times n matrix A=(a_) associated with the character \chi_\lambda is defined as the expression :\operatorname_\lambda(A)=\sum_ \chi_\lambda(\sigma) a_ a_ \cdots a_. Examples The determinant is a special case of the immanant, where \chi_\lambda is the alternating character \sgn, of ''S''''n'', defined by the parity of a permutation. The permanent is the case where \chi_\lambda is the trivial character, which is identically equal to 1. For example, for 3 \times 3 matrices, there are three irreducible representations of S_3, as shown in the character table: As stated above, \chi_1 produces th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Schur Polynomial
In mathematics, Schur polynomials, named after Issai Schur, are certain symmetric polynomials in ''n'' variables, indexed by partitions, that generalize the elementary symmetric polynomials and the complete homogeneous symmetric polynomials. In representation theory they are the characters of polynomial irreducible representations of the general linear groups. The Schur polynomials form a linear basis for the space of all symmetric polynomials. Any product of Schur polynomials can be written as a linear combination of Schur polynomials with non-negative integral coefficients; the values of these coefficients is given combinatorially by the Littlewood–Richardson rule. More generally, skew Schur polynomials are associated with pairs of partitions and have similar properties to Schur polynomials. Definition (Jacobi's bialternant formula) Schur polynomials are indexed by integer partitions. Given a partition , where , and each is a non-negative integer, the functions a_ (x_ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quasideterminant
In mathematics, the quasideterminant is a replacement for the determinant for matrices with noncommutative entries. Example 2 × 2 quasideterminants are as follows: : \left, \begin a_ & a_ \\ a_ & a_ \end \_ = a_ - a_^a_ \qquad \left, \begin a_ & a_ \\ a_ & a_ \end \_ = a_ - a_^a_. In general, there are ''n''2 quasideterminants defined for an ''n'' × ''n'' matrix (one for each position in the matrix), but the presence of the inverted terms above should give the reader pause: they are not always defined, and even when they are defined, they do not reduce to determinants when the entries commute. Rather, : \left, A\_ = (-1)^ \frac , where A^ means delete the ''i''th row and ''j''th column from ''A''. The 2\times2 examples above were introduced between 1926 and 1928 by Richardson and Heyting, but they were marginalized at the time because they were not polynomials in the entries of A. These examples were redisc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1881 Births
Events January–March * January 1– 24 – Siege of Geok Tepe: Russian troops under General Mikhail Skobelev defeat the Turkomans. * January 13 – War of the Pacific – Battle of San Juan and Chorrillos: The Chilean army defeats Peruvian forces. * January 15 – War of the Pacific – Battle of Miraflores: The Chileans take Lima, capital of Peru, after defeating its second line of defense in Miraflores. * January 24 – William Edward Forster, chief secretary for Ireland, introduces his Coercion Bill, which temporarily suspends habeas corpus so that those people suspected of committing an offence can be detained without trial; it goes through a long debate before it is accepted February 2. * January 25 – Thomas Edison and Alexander Graham Bell form the Oriental Telephone Company. * February 13 – The first issue of the feminist newspaper ''La Citoyenne'' is published by Hubertine Auclert. * February 16 – ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
