High Quality Content by WIKIPEDIA articles! In mathematics, matrix calculus is a specialized notation for doing multivariable calculus, especially over spaces of matrices, where it defines the matrix derivative. This notation is well-suited to describing systems of differential equations, and taking derivatives of matrix-valued functions with respect to matrix variables. This notation is commonly used in statistics and engineering, while the tensor index notation is preferred in physics. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1308-6725-6
Издательство: Книга по требованию
Дата выхода: июль 2011

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and of its derivatives of various orders. A matrix differential equation is one containing more than one function stacked into vector form with a matrix relating the functions to their derivatives. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1328-8116-8
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! Une matrice de controle est un concept de theorie des codes utilise dans le cas des codes correcteurs lineaires. Elle correspond a la matrice d'une application lineaire ayant pour noyau le code. La notion de matrice de controle possede a la fois un interet theorique dans le cadre de l'etude des codes correcteurs, par exemple pour offrir des criteres sur la distance minimale du code ou une condition necessaire et suffisante pour qu'un code soit parfait et un interet pratique pour un decodage efficace. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения...

ISBN: 978-6-1318-9348-3
Издательство: Книга по требованию
Дата выхода: июль 2011

ISBN: 978-6-1306-7954-5
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Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, in particular linear algebra, the matrix determinant lemma computes the determinant of the sum of an invertible matrix A and the dyadic product, u vT, of a column vector u and a row vector vT. Suppose A is an invertible square matrix and u, v are column vectors. Then the matrix determinant lemma states that. Here, uvT is the dyadic product of two vectors u and v. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1338-3307-4
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Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, a matrix unit is an idealisation of the concept of a matrix, with a focus on the algebraic properties of matrix multiplication. The topic is comparatively obscure within linear algebra, because it entirely ignores the numeric properties of matrices; it is mostly encountered in the context of abstract algebra, especially the theory of semigroups. Despite the name, matrix units are not the same as unit matrices or unitary matrices. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1338-1703-6
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Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, matrix addition is the operation of adding two matrices by adding the corresponding entries together. However, there is another operation which could also be considered as a kind of addition for matrices. The usual matrix addition is defined for two matrices of the same dimensions. The sum of two m-by-n matrices A and B, denoted by A + B, is again an m-by-n matrix computed by adding corresponding elements. We can also subtract one matrix from another, as long as they have the same dimensions. A - B is computed by subtracting corresponding elements of A and B, and has the same dimensions as A and B. Данное издание не является оригинальным....

ISBN: 978-6-1337-6542-9
Издательство: Книга по требованию
Дата выхода: июль 2011

Matrix mechanics. Schrodinger picture, Interaction picture, Quantum mechanics, Schrodinger equation, Bra-ket notation, Introduction to quantum mechanics, Old quantum theory, Fourier series, Quantum computer Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1300-4148-9
Издательство: Книга по требованию
Дата выхода: июль 2011

The aim of this book is the study of graph dynamics, also known as graph rewriting. Matrix Graph Grammars proposes a new approach to the many open problems that exist in the subject. From the point of view of a computer scientist, graph grammars are a natural generalization of Chomsky grammars, for which a purely algebraic approach does not exist up to now. A Chomsky (or string) grammar is, roughly speaking, a precise description of a formal language (which in essence is a set of strings). On a more discrete mathematical style, it can be said that graph grammars -- Matrix Graph Grammars in particular -- study the dynamics of graphs in contrast to the more common static approach, which mainly deals with properties such as coloring....

ISBN: 978-3-6392-1255-6
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, the Maurer–Cartan form for a Lie group G is a distinguished differential one-form on G that carries within itself the basic infinitesimal information about the structure of G. It was much used by Elie Cartan as a basic ingredient of his method of moving frames, and bears his name together with that of Ludwig Maurer. As a one-form, the Maurer–Cartan form is peculiar in that it takes its values in the Lie algebra associated to the Lie group G. The Lie algebra is identified with the tangent space of G at the identity, denoted TeG. The Maurer–Cartan form ? is thus a one-form defined globally on G which is a linear mapping of the tangent space TgG at each g ? G into TeG....

ISBN: 978-6-1311-5156-9
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Дата выхода: июль 2011

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, the Maurer–Cartan form for a Lie group G is a distinguished differential one-form on G that carries within itself the basic infinitesimal information about the structure of G. It was much used by Elie Cartan as a basic ingredient of his method of moving frames, and bears his name together with that of Ludwig Maurer. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1328-5318-9
Издательство: Книга по требованию
Дата выхода: июль 2011

Maurice Frechet (September 2, 1878 – June 4, 1973) was a French mathematician. He made major contributions to the topology of point sets and introduced the entire concept of metric spaces. He also made several important contributions to the field of statistics and probability, as well as calculus. His dissertation opened the entire field of functionals on metric spaces and introduced the notion of compactness. Independently of Riesz, he discovered the representation theorem in the space of Lebesgue square integrable functions. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1307-1977-7
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Machgielis (Max) Euwe (May 20, 1901 – November 26, 1981) was a Dutch chess Grandmaster, mathematician, and author. He was the fifth player to become World Chess Champion (1935–1937). Euwe also served as President of FIDE, the World Chess Federation, from 1970 to 1978. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1337-5079-1
Издательство: Книга по требованию
Дата выхода: июль 2011

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. High Quality Content by WIKIPEDIA articles! Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Charles Max Mason (October 26, 1877, Madison, Wisconsin – March 23, 1961, Claremont, California, better known as Max Mason) was an American mathematician. Mason was president of the University of Chicago (1925–1929) and president of the Rockefeller Foundation (1929–1936). Mason's mathematical research interests included differential equations, the calculus of variations, and electromagnetic theory. Данное издание не...

ISBN: 978-6-1338-1073-0
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! Max Noether (24 September 1844 - 13 December 1921) was a German mathematician who worked on algebraic geometry and the theory of algebraic functions. He has been called "one of the finest mathematicians of the nineteenth century". Max Noether was born in Mannheim in 1844, to a Jewish family of wealthy wholesale hardware dealers. His grandfather, Elias Samuel, had started the business in Bruchsal in 1797. In 1809 Grand Duchy of Baden established a "Tolerance Edict", which assigned a hereditary surname to the male head of every Jewish family which did not already possess one. Thus the Samuels became the Noether family, and as part of this Christianization of names, their son Hertz (Max's father)...

ISBN: 978-6-1316-0979-4
Издательство: Книга по требованию
Дата выхода: июль 2011

Network ?ow theory constitutes a thoroughly studied mathematical ?eld which is widely applied in practice in areas as diverse as economics, traffic routing, or telecommunication. Interestingly, networks can be discussed equally well by using methods from graph theory or from linear programming (LP). Both of these approaches have advantages and disadvantages, and are usually treated using their own terminology and techniques. In this piece of work, the notions of network theory are developed such that the combinatorial and the LP point of view can be presented as homogeneously as possible. All de?nitions and theorems are formulated using a fairly general network model that lends itself well to both disciplines. After the introduction of...

ISBN: 978-3-6392-0932-7
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Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In optimization theory, the max-flow min-cut theorem states that in a flow network, the maximum amount of flow passing from the source to the sink is equal to the minimum capacity that needs to be removed from the network so that no flow can pass from the source to the sink. The max-flow min-cut theorem is a special case of the duality theorem and can be used to derive the Menger's theorem and the Konig-Egervary Theorem. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1317-6965-8
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Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! For a graph, a maximum cut is a cut whose size is not smaller than the size of any other cut. The problem of finding a maximum cut in a graph is known as the max-cut problem.The problem can be stated simply as follows. One wants a subset S of the vertex set such that the number of edges between S and the complementary subset is as large as possible. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1327-4532-3
Издательство: Книга по требованию
Дата выхода: июль 2011

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. The maximal ergodic theorem is a theorem in ergodic theory, a discipline within mathematics. Suppose that is a probability space, that is a measure-preserving transformation, and that . Define f * by Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1328-6895-4
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Дата выхода: июль 2011

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. The maximum theorem provides conditions for the continuity of an optimized function and the set of its maximizers as a parameter changes. The statement was first proven by Claude Berge in 1959. The theorem is primarily used in mathematical economics. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1328-3674-8
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, a maximal compact subgroup K of a topological group G is a subgroup K that is a compact space, in the subspace topology, and maximal amongst such subgroups. A maximal compact subgroup does not always exist for a general Lie group, but does exist for a semisimple Lie group, and they play an important role in their theory. Maximal compact subgroups are not in general unique, but are unique up to conjugation – they are essentially unique. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1327-9807-7
Издательство: Книга по требованию
Дата выхода: июль 2011

ISBN: 978-6-1326-3087-2
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In the mathematical theory of compact Lie groups a special role is played by torus subgroups, in particular by the maximal torus subgroups. A torus in a Lie group G is a compact, connected, abelian Lie subgroup of G (and therefore isomorphic to the standard torus Tn). A maximal torus is one which is maximal among such subgroups. That is, T is a maximal torus if for any other torus T? containing T we have T = T?. Every torus is contained in a maximal torus simply by dimensional considerations. A noncompact Lie group need not have any nontrivial tori (e.g. Rn). The dimension of a maximal torus in G is called the rank of G. The rank is well-defined since all maximal tori turn out to be conjugate....

ISBN: 978-6-1327-8026-3
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In graph theory, a maximal independent set or maximal stable set is an independent set that is not a subset of any other independent set. That is, it is a set S such that every edge of the graph has at least one endpoint not in S and every vertex not in S has at least one neighbor in S. A maximal independent set is also a dominating set in the graph, and every dominating set that is independent must be maximal independent, so maximal independent sets are also called independent dominating sets. A graph may have many maximal independent sets of widely varying sizes a largest maximal independent set is called a maximum independent set. For example, in the graph P3, a path with three vertices a,...

ISBN: 978-6-1326-0837-6
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Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In optimization theory, the maximum flow problem is to find a feasible flow through a single-source, single-sink flow network that is maximum. The maximum flow problem can be seen as a special case of more complex network flow problems, such as the circulation problem. The maximum value of an s-t flow is equal to the minimum capacity of an s-t cut in the network, as stated in the max-flow min-cut theorem. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1327-4743-3
Издательство: Книга по требованию
Дата выхода: июль 2011