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List Of Things Named After James Joseph Sylvester
The mathematician J. J. Sylvester was known for his ability to coin new names and new notation for mathematical objects, not based on his own name. Nevertheless, many objects and results in mathematics have come to be named after him: *The Sylvester–Gallai theorem, on the existence of a line with only two of ''n'' given points. **Sylvester–Gallai configuration, a set of points and lines without any two-point lines. **Sylvester matroid, a matroid without any two-point lines. *Sylvester's determinant identity. *Sylvester's matrix theorem, a.k.a. Sylvester's formula, for a matrix function in terms of eigenvalues. *Sylvester's theorem on the product of ''k'' consecutive integers > ''k'', that generalizes Bertrand's postulate. *Sylvester's law of inertia a.k.a. Sylvester's rigidity theorem, about the signature of a quadratic form. *Sylvester's identity about determinants of submatrices. *Sylvester's criterion, a characterization of positive-definite Hermitian matrices. *Sylvester do ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MathSciNet
MathSciNet is a searchable online bibliographic database created by the American Mathematical Society in 1996. It contains all of the contents of the journal ''Mathematical Reviews'' (MR) since 1940 along with an extensive author database, links to other MR entries, citations, full journal entries, and links to original articles. It contains almost 3.6 million items and over 2.3 million links to original articles. Along with its parent publication ''Mathematical Reviews'', MathSciNet has become an essential tool for researchers in the mathematical sciences. Access to the database is by subscription only and is not generally available to individual researchers who are not affiliated with a larger subscribing institution. For the first 40 years of its existence, traditional typesetting was used to produce the Mathematical Reviews journal. Starting in 1980 bibliographic information and the reviews themselves were produced in both print and electronic form. This formed the basis of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sylvester Cyclotomic Number
Sylvester or Silvester is a name derived from the Latin adjective ''silvestris'' meaning "wooded" or "wild", which derives from the noun ''silva'' meaning "woodland". Classical Latin spells this with ''i''. In Classical Latin, ''y'' represented a separate sound distinct from ''i'', not a native Latin sound but one used in transcriptions of foreign words. After the Classical period ''y'' was pronounced as ''i''. Spellings with ''Sylv-'' in place of ''Silv-'' date from after the Classical period. Given name *Sylvester of Marsico (c. 1100–1162), Count of Marsico in the Kingdom of Sicily * Silvester Ashioya (born 1948), Kenyan hockey player *Silvester Bolam (1905–1953), British newspaper editor *Silvester Brito (1937–2018), American poet and academic *Sylvester Croom (born 1954), American football coach and former player *Silvester Diggles (1817–1880), Australian musician and ornithologist *Silvester Fernandes (born 1936), Kenyan hockey player *Silvester Gardiner (1708–178 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hadamard Matrix
In mathematics, a Hadamard matrix, named after the French mathematician Jacques Hadamard, is a square matrix whose entries are either +1 or −1 and whose rows are mutually orthogonal. In geometric terms, this means that each pair of rows in a Hadamard matrix represents two perpendicular vectors, while in combinatorial terms, it means that each pair of rows has matching entries in exactly half of their columns and mismatched entries in the remaining columns. It is a consequence of this definition that the corresponding properties hold for columns as well as rows. The ''n''-dimensional parallelotope spanned by the rows of an ''n''×''n'' Hadamard matrix has the maximum possible ''n''-dimensional volume among parallelotopes spanned by vectors whose entries are bounded in absolute value by 1. Equivalently, a Hadamard matrix has maximal determinant among matrices with entries of absolute value less than or equal to 1 and so is an extremal solution of Hadamard's maximal determina ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coin Problem
The coin problem (also referred to as the Frobenius coin problem or Frobenius problem, after the mathematician Ferdinand Frobenius) is a mathematical problem that asks for the largest monetary amount that cannot be obtained using only coins of specified denominations, for example, the largest amount that cannot be obtained using only coins of 3 and 5 units is 7 units. The solution to this problem for a given set of coin denominations is called the Frobenius number of the set. The Frobenius number exists as long as the set of coin denominations has no common divisor greater than 1. There is an explicit formula for the Frobenius number when there are only two different coin denominations, ''x'' and ''y'': the Frobenius number is then ''xy'' − ''x'' − ''y''. If the number of coin denominations is three or more, no explicit formula is known. However, for any fixed number of coin denominations, there is an algorithm computing the Frobenius number in polynomial time (in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
JavaScript
JavaScript (), often abbreviated as JS, is a programming language that is one of the core technologies of the World Wide Web, alongside HTML and CSS. As of 2022, 98% of Website, websites use JavaScript on the Client (computing), client side for Web page, webpage behavior, often incorporating third-party Library (computing), libraries. All major Web browser, web browsers have a dedicated JavaScript engine to execute the Source code, code on User (computing), users' devices. JavaScript is a High-level programming language, high-level, often Just-in-time compilation, just-in-time compiled language that conforms to the ECMAScript standard. It has dynamic typing, Prototype-based programming, prototype-based object-oriented programming, object-orientation, and first-class functions. It is Programming paradigm, multi-paradigm, supporting Event-driven programming, event-driven, functional programming, functional, and imperative programming, imperative programming paradigm, programmin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sylvester Medal
The Sylvester Medal is a bronze medal awarded by the Royal Society (London) for the encouragement of mathematical research, and accompanied by a £1,000 prize. It was named in honour of James Joseph Sylvester, the Savilian Professor of Geometry at the University of Oxford in the 1880s, and first awarded in 1901, having been suggested by a group of Sylvester's friends (primarily Raphael Meldola) after his death in 1897. Initially awarded every three years with a prize of around £900, the Royal Society have announced that starting in 2009 it will be awarded every two years instead, and is to be aimed at 'early to mid career stage scientist' rather than an established mathematician. The award winner is chosen by the Society's A-side awards committee, which handles physical rather than biological science awards. , 45 medals have been awarded, of which all but 10 have been awarded to citizens of the United Kingdom, two to citizens of France and United States, and one medal each has be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sylvester (crater)
Sylvester is a lunar impact crater that is located near the north pole of the Moon, along the northern limb in the libration zone. It lies just to the south-southeast of the craters Grignard and Hermite; the latter of which is within one crater diameter of the pole. South of Sylvester is Pascal Pascal, Pascal's or PASCAL may refer to: People and fictional characters * Pascal (given name), including a list of people with the name * Pascal (surname), including a list of people and fictional characters with the name ** Blaise Pascal, Fren .... Due to its location, Sylvester receives sunlight at only a low angle. This crater is generally circular, with a sharp-edged rim that has received only a moderate amount of wear. There are no craters of note along the rim, although Sylvester intrudes into a smaller, shallow-rimmed crater to the southeast. The interior floor is relatively flat, but punctuated by several tiny craters. At the midpoint is a small central peak. Satellite craters ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sylver Coinage
Sylver coinage is a mathematical game for two players, invented by John H. Conway. It is discussed in chapter 18 of '' Winning Ways for Your Mathematical Plays''. This article summarizes that chapter. The two players take turns naming positive integers greater than 1 that are not the sum of nonnegative multiples of previously named integers. The player who cannot name such a number loses. For instance, if player A opens with 2, B can win by naming 3. Sylver coinage is named after James Joseph Sylvester, who proved that if ''a'' and ''b'' are relatively prime positive integers, then (''a'' − 1)(''b'' − 1) − 1 is the largest number that is not a sum of nonnegative multiples of ''a'' and ''b''. Thus, if ''a'' and ''b'' are the first two moves in a game of sylver coinage, this formula gives the largest number that can still be played. More generally, if the greatest common divisor of the moves played so far is ''g'', then only finitely many ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rank (linear Algebra)
In linear algebra, the rank of a matrix is the dimension of the vector space generated (or spanned) by its columns. p. 48, § 1.16 This corresponds to the maximal number of linearly independent columns of . This, in turn, is identical to the dimension of the vector space spanned by its rows. Rank is thus a measure of the " nondegenerateness" of the system of linear equations and linear transformation encoded by . There are multiple equivalent definitions of rank. A matrix's rank is one of its most fundamental characteristics. The rank is commonly denoted by or ; sometimes the parentheses are not written, as in .Alternative notation includes \rho (\Phi) from and . Main definitions In this section, we give some definitions of the rank of a matrix. Many definitions are possible; see Alternative definitions for several of these. The column rank of is the dimension of the column space of , while the row rank of is the dimension of the row space of . A fundamental result in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Greedy Algorithm For Egyptian Fractions
In mathematics, the greedy algorithm for Egyptian fractions is a greedy algorithm, first described by Fibonacci, for transforming rational numbers into Egyptian fractions. An Egyptian fraction is a representation of an irreducible fraction as a sum of distinct unit fractions, such as . As the name indicates, these representations have been used as long ago as ancient Egypt, but the first published systematic method for constructing such expansions was described in 1202 in the ''Liber Abaci'' of Leonardo of Pisa (Fibonacci). It is called a greedy algorithm because at each step the algorithm chooses greedily the largest possible unit fraction that can be used in any representation of the remaining fraction. Fibonacci actually lists several different methods for constructing Egyptian fraction representations. He includes the greedy method as a last resort for situations when several simpler methods fail; see Egyptian fraction for a more detailed listing of these methods. As Salzer ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sylvester Equation
In mathematics, in the field of control theory, a Sylvester equation is a Matrix (mathematics), matrix equation of the form: :A X + X B = C. Then given matrices ''A'', ''B'', and ''C'', the problem is to find the possible matrices ''X'' that obey this equation. All matrices are assumed to have coefficients in the complex numbers. For the equation to make sense, the matrices must have appropriate sizes, for example they could all be square matrices of the same size. But more generally, ''A'' and ''B'' must be square matrices of sizes ''n'' and ''m'' respectively, and then ''X'' and ''C'' both have ''n'' rows and ''m'' columns. A Sylvester equation has a unique solution for ''X'' exactly when there are no common eigenvalues of ''A'' and −''B''. More generally, the equation ''AX'' + ''XB'' = ''C'' has been considered as an equation of bounded operators on a (possibly infinite-dimensional) Banach space. In this case, the condition for the uniqueness of a solut ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
