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Author: Apoorva Khare
Publisher: Cambridge University Press
ISBN: 9781108792042
Category : Mathematics
Languages : en
Pages : 300
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Book Description
Matrices and kernels with positivity structures, and the question of entrywise functions preserving them, have been studied throughout the 20th century, attracting recent interest in connection to high-dimensional covariance estimation. This is the first book to systematically develop the theoretical foundations of the entrywise calculus, focusing on entrywise operations - or transforms - of matrices and kernels with additional structure, which preserve positive semidefiniteness. Designed as an introduction for students, it presents an in-depth and comprehensive view of the subject, from early results to recent progress. Topics include: structural results about, and classifying the preservers of positive semidefiniteness and other Loewner properties (monotonicity, convexity, super-additivity); historical connections to metric geometry; classical connections to moment problems; and recent connections to combinatorics and Schur polynomials. Based on the author's course, the book is structured for use as lecture notes, including exercises for students, yet can also function as a comprehensive reference text for experts.
Author: Apoorva Khare
Publisher: Cambridge University Press
ISBN: 9781108792042
Category : Mathematics
Languages : en
Pages : 300
Get Book Here
Book Description
Matrices and kernels with positivity structures, and the question of entrywise functions preserving them, have been studied throughout the 20th century, attracting recent interest in connection to high-dimensional covariance estimation. This is the first book to systematically develop the theoretical foundations of the entrywise calculus, focusing on entrywise operations - or transforms - of matrices and kernels with additional structure, which preserve positive semidefiniteness. Designed as an introduction for students, it presents an in-depth and comprehensive view of the subject, from early results to recent progress. Topics include: structural results about, and classifying the preservers of positive semidefiniteness and other Loewner properties (monotonicity, convexity, super-additivity); historical connections to metric geometry; classical connections to moment problems; and recent connections to combinatorics and Schur polynomials. Based on the author's course, the book is structured for use as lecture notes, including exercises for students, yet can also function as a comprehensive reference text for experts.
Author: H. Garth Dales
Publisher: American Mathematical Soc.
ISBN: 1470446928
Category : Education
Languages : en
Pages : 296
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Book Description
This volume contains the proceedings of the Conference on Complex Analysis and Spectral Theory, in celebration of Thomas Ransford's 60th birthday, held from May 21–25, 2018, at Laval University, Québec, Canada. Spectral theory is the branch of mathematics devoted to the study of matrices and their eigenvalues, as well as their infinite-dimensional counterparts, linear operators and their spectra. Spectral theory is ubiquitous in science and engineering because so many physical phenomena, being essentially linear in nature, can be modelled using linear operators. On the other hand, complex analysis is the calculus of functions of a complex variable. They are widely used in mathematics, physics, and in engineering. Both topics are related to numerous other domains in mathematics as well as other branches of science and engineering. The list includes, but is not restricted to, analytical mechanics, physics, astronomy (celestial mechanics), geology (weather modeling), chemistry (reaction rates), biology, population modeling, economics (stock trends, interest rates and the market equilibrium price changes). There are many other connections, and in recent years there has been a tremendous amount of work on reproducing kernel Hilbert spaces of analytic functions, on the operators acting on them, as well as on applications in physics and engineering, which arise from pure topics like interpolation and sampling. Many of these connections are discussed in articles included in this book.
Author: Charles R. Johnson
Publisher: Cambridge University Press
ISBN: 1108478719
Category : Mathematics
Languages : en
Pages : 223
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Book Description
This comprehensive reference, for mathematical, engineering and social scientists, covers matrix positivity classes and their applications.
Author: Felix Fischer
Publisher: Cambridge University Press
ISBN: 1009490532
Category : Mathematics
Languages : en
Pages : 305
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Book Description
This volume contains surveys of current research directions in combinatorics written by leading researchers in their fields.
Author: Frank Oertel
Publisher: Springer Nature
ISBN: 3031572017
Category :
Languages : en
Pages : 238
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Book Description
Author: R. A. Bailey
Publisher: Cambridge University Press
ISBN: 1009465945
Category : Mathematics
Languages : en
Pages : 452
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Book Description
This collection of four short courses looks at group representations, graph spectra, statistical optimality, and symbolic dynamics, highlighting their common roots in linear algebra. It leads students from the very beginnings in linear algebra to high-level applications: representations of finite groups, leading to probability models and harmonic analysis; eigenvalues of growing graphs from quantum probability techniques; statistical optimality of designs from Laplacian eigenvalues of graphs; and symbolic dynamics, applying matrix stability and K-theory. An invaluable resource for researchers and beginning Ph.D. students, this book includes copious exercises, notes, and references.
Author: Chris Godsil
Publisher: Cambridge University Press
ISBN: 1009261681
Category : Computers
Languages : en
Pages : 151
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Book Description
Explore the mathematics arising from discrete quantum walks in this introduction to a rapidly developing area.
Author: Alexandru Aleman
Publisher: Springer
ISBN: 3030146405
Category : Mathematics
Languages : en
Pages : 283
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Book Description
This book contains both expository articles and original research in the areas of function theory and operator theory. The contributions include extended versions of some of the lectures by invited speakers at the conference in honor of the memory of Serguei Shimorin at the Mittag-Leffler Institute in the summer of 2018. The book is intended for all researchers in the fields of function theory, operator theory and complex analysis in one or several variables. The expository articles reflecting the current status of several well-established and very dynamical areas of research will be accessible and useful to advanced graduate students and young researchers in pure and applied mathematics, and also to engineers and physicists using complex analysis methods in their investigations.
Author: Alexander A. Ivanov
Publisher: Cambridge University Press
ISBN: 1009338048
Category : Mathematics
Languages : en
Pages : 583
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Book Description
The current state of knowledge on the Monster group, including Majorana theory, Vertex Operator Algebras, Moonshine and maximal subgroups.
Author: Kelli Francis-Staite
Publisher: Cambridge University Press
ISBN: 1009400169
Category : Mathematics
Languages : en
Pages : 223
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Book Description
Crossing the boundary between differential and algebraic geometry in order to study singular spaces, this book introduces 'C∞-schemes with corners'.
