Related Research Articles
Linear algebra is the branch of mathematics concerning linear equations such as:
In mathematics, and in particular linear algebra, the Moore–Penrose inverse of a matrix , often called the pseudoinverse, is the most widely known generalization of the inverse matrix. It was independently described by E. H. Moore in 1920, Arne Bjerhammar in 1951, and Roger Penrose in 1955. Earlier, Erik Ivar Fredholm had introduced the concept of a pseudoinverse of integral operators in 1903. The terms pseudoinverse and generalized inverse are sometimes used as synonyms for the Moore–Penrose inverse of a matrix, but sometimes applied to other elements of algebraic structures which share some but not all properties expected for an inverse element.
Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures.
The Bôcher Memorial Prize was founded by the American Mathematical Society in 1923 in memory of Maxime Bôcher with an initial endowment of $1,450. It is awarded every three years for a notable research work in analysis that has appeared during the past six years. The work must be published in a recognized, peer-reviewed venue. The current award is $5,000.
In mathematics, secondary calculus is a proposed expansion of classical differential calculus on manifolds, to the "space" of solutions of a (nonlinear) partial differential equation. It is a sophisticated theory at the level of jet spaces and employing algebraic methods.
In mathematics, especially in linear algebra and matrix theory, a centrosymmetric matrix is a matrix which is symmetric about its center.
Philippe G. Ciarlet is a French mathematician, known particularly for his work on mathematical analysis of the finite element method. He has contributed also to elasticity, to the theory of plates and shells and differential geometry.
The stability problem of functional equations originated from a question of Stanisław Ulam, posed in 1940, concerning the stability of group homomorphisms. In the next year, Donald H. Hyers gave a partial affirmative answer to the question of Ulam in the context of Banach spaces in the case of additive mappings, that was the first significant breakthrough and a step toward more solutions in this area. Since then, a large number of papers have been published in connection with various generalizations of Ulam's problem and Hyers's theorem. In 1978, Themistocles M. Rassias succeeded in extending Hyers's theorem for mappings between Banach spaces by considering an unbounded Cauchy difference subject to a continuity condition upon the mapping. He was the first to prove the stability of the linear mapping. This result of Rassias attracted several mathematicians worldwide who began to be stimulated to investigate the stability problems of functional equations.
A classical problem of Stanislaw Ulam in the theory of functional equations is the following: When is it true that a function which approximately satisfies a functional equation E must be close to an exact solution of E? In 1941, Donald H. Hyers gave a partial affirmative answer to this question in the context of Banach spaces. This was the first significant breakthrough and a step towards more studies in this domain of research. Since then, a large number of papers have been published in connection with various generalizations of Ulam's problem and Hyers' theorem. In 1978, Themistocles M. Rassias succeeded in extending the Hyers' theorem by considering an unbounded Cauchy difference. He was the first to prove the stability of the linear mapping in Banach spaces. In 1950, T. Aoki had provided a proof of a special case of the Rassias' result when the given function is additive. For an extensive presentation of the stability of functional equations in the context of Ulam's problem, the interested reader is referred to the recent book of S.-M. Jung, published by Springer, New York, 2011.
Mathematics is a broad subject that is commonly divided in many areas that may be defined by their objects of study, by the used methods, or by both. For example, analytic number theory is a subarea of number theory devoted to the use of methods of analysis for the study of natural numbers.
Eldon Robert Hansen is an American mathematician and author who has published in global optimization theory and interval arithmetic.
The following is a timeline of numerical analysis after 1945, and deals with developments after the invention of the modern electronic computer, which began during Second World War. For a fuller history of the subject before this period, see timeline and history of mathematics.
Gerhard Huisken is a German mathematician whose research concerns differential geometry and partial differential equations. He is known for foundational contributions to the theory of the mean curvature flow, including Huisken's monotonicity formula, which is named after him. With Tom Ilmanen, he proved a version of the Riemannian Penrose inequality, which is a special case of the more general Penrose conjecture in general relativity.
Julius Bogdan Borcea was a Romanian Swedish mathematician. His scientific work included vertex operator algebra and zero distribution of polynomials and entire functions, via correlation inequalities and statistical mechanics.
Alexander Nikolaevich Varchenko is a Soviet and Russian mathematician working in geometry, topology, combinatorics and mathematical physics.
Tamar Debora Ziegler is an Israeli mathematician known for her work in ergodic theory, combinatorics and number theory. She holds the Henry and Manya Noskwith Chair of Mathematics at the Einstein Institute of Mathematics at the Hebrew University.
Alexander G. Ramm is an American mathematician. His research focuses on differential and integral equations, operator theory, ill-posed and inverse problems, scattering theory, functional analysis, spectral theory, numerical analysis, theoretical electrical engineering, signal estimation, and tomography.
Thomas J. Laffey is an Irish mathematician known for his contributions to group theory and matrix theory. His entire career has been spent at University College Dublin (UCD), where he served two terms as head of the school of mathematics. While he formally retired in 2009, he remains active in research and publishing. The journal Linear Algebra and Its Applications had a special issue to mark his 65th birthday. He received the Hans Schneider Prize in 2013. In May 2019 at UCD, the International Conference on Linear Algebra and Matrix Theory held a celebration to honor Professor Laffey on his 75th birthday.
Joel Spruck is a mathematician, J. J. Sylvester Professor of Mathematics at Johns Hopkins University, whose research concerns geometric analysis and elliptic partial differential equations. He obtained his PhD from Stanford University with the supervision of Robert S. Finn in 1971.
References
- ↑ Ben-Israel, A. "Personal webpage".
- ↑ Jonathan S. Golan (23 April 2012). The Linear Algebra a Beginning Graduate Student Ought to Know. Springer Science & Business Media. pp. 445–. ISBN 978-94-007-2636-9.
- ↑ "Matrix Volume" (PDF). GI-LECTURE-5.dvi.
- ↑ Rehman, Abdur; Kyrchei, Ivan; Akram, Muhammad; Ali, Ilyas; Shakoor, Abdul (19 August 2019). "Least-Norm of the General Solution to Some System of Quaternion Matrix Equations and Its Determinantal Representations". Abstract and Applied Analysis. 2019: 1–18. doi: 10.1155/2019/9072690 .
- ↑ "Ordered Incidence Geometry" (PDF). GI-LECTURE-5.dvi.
- 1 2 Christopher Hollings (16 July 2014). Mathematics across the Iron Curtain: A History of the Algebraic Theory of Semigroups. American Mathematical Society. pp. 378–. ISBN 978-1-4704-1493-1.
- ↑ K.P.S. Bhaskara Rao (2 September 2003). Theory of Generalized Inverses Over Commutative Rings. CRC Press. pp. 10–. ISBN 978-0-203-21887-7.
