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Books on the topic 'Symmetric matrices'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 April 2022

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1

Parlett, Beresford N. The symmetric eigenvalue problem. Society for Industrial and Applied Mathematics, 1998.

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2

Tadmor, Eitan. Complex symmetric matrices with strongly stable iterates. National Aeronautics and Space Administration, Langley Research Center, 1985.

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3

Tadmor, Eitan. Complex symmetric matrices with strongly stable iterates. National Aeronautics and Space Administration, Langley Research Center, 1985.

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4

A, Willoughby Ralph, ed. Lanczos algorithms for large symmetric eigenvalue computations. Birkhäuser, 1985.

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5

Jones, Mark T. Bunch-Kaufman factorization for real symmetric indefinite banded matrices. ICASE, 1989.

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6

Freund, Roland W. Conjugate gradient type methods for linear systems with complex symmetric coefficient matrices. Research Institute for Advanced Computer Science, NASA Ames Research Center, 1989.

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7

Kandasamy, W. B. Vasantha. Super linear algebra. Infolearnquest, 2008.

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8

Ha, Xian Wei. Invariant measure on sums of symmetric matrices and its singularities and zero points. [s.n.], 1994.

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9

Bell, Kolbein. Eigensolvers for structural problems: Some algorithms for symmetric eigenvalue problems and their merits. Delft Univ. Press, 1998.

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10

Overton, Michael L. Optimality conditions and duality theory for minimizing sums of the largest eigenvalues of symmetric matrices. Courant Institute of Mathematical Sciences, New York University, 1991.

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11

Dinkevich, Solomon. Explicit block diagonal decomposition of block matrices corresponding to symmetric and regular structures of finite size. Courant Institute of Mathematical Sciences, New York University, 1986.

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12

Gill, Doron. An O(N2) method for computing the Eigensystem of N x N symmetric tridiagonal matrices by the divide and conquer approach. ICASE, 1988.

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13

Zloković, Đorđe. Group supermatrices in finite element analysis. Ellis Horwood, 1992.

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14

Zloković, Đorđe. Group supermatrices in finite element analysis. E. Horwood, 1992.

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15

Keating, Jonathan P. Discrete symmetries and spectral statistics. Hewlett Packard, 1996.

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16

Spitzer-Shamir, Tzila. Masaʻ be-ʻolamot mufshaṭim: Mifgash aḥer ʻim matemaṭiḳah. Hotsaʼat sefarim ʻa. sh. Y.L. Magnes, ha-Universiṭah ha-ʻIvrit, 1996.

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17

Spherical tensor operators: Tables of matrix elements and symmetries. World Scientific, 1990.

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18

Terras, Audrey. Harmonic analysis on symmetric spaces and applications. Springer-Verlag, 1988.

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19

Harmonic analysis on symmetric spaces and applications. Springer-Verlag, 1985.

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20

Gunzburger, Max D. On substructuring algorithms and solution techniques for the numerical approximation of partial differential equations. National Aeronautics and Space Administration, 1986.

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21

Guattery, Stephen. Graph embedding techniques for bounding condition numbers of incomplete factor preconditioners. Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1997.

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22

Rodríguez, Rubí E., 1953- editor of compilation, ed. Riemann and Klein surfaces, automorphisms, symmetries and moduli spaces: Conference in honor of Emilio Bujalance on Riemann and Klein surfaces, symmetries and moduli spaces, June 24-28, 2013, Linköping University, Linköping, Sweden. American Mathematical Society, 2014.

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23

Center, Langley Research, and Institute for Computer Applications in Science and Engineering., eds. Complex symmetric matrices with strongly stable iterates. National Aeronautics and Space Administration, Langley Research Center, 1985.

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24

Institute for Computer Applications in Science and Engineering., ed. Graph embeddings, symmetric real matrices, and generalized inverses. Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1998.

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25

L, Patrick Merrell, and Langley Research Center, eds. Factoring symmetric indefinite matrices on high-performance architectures. National Aeronautics and Space Administration, Langley Research Center, 1990.

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26

Institute for Computer Applications in Science and Engineering., ed. Graph embeddings, symmetric real matrices, and generalized inverses. Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1998.

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27

An O(N) method for computing the eigensystem of N x N symmetric tridiagonal matrices by the divide and conquer approach. National Aeronautics and Space Administration, Langley Research Center, 1988.

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28

Haag, Jeffrey Burgess. Generic (GR) decomposition algorithms for the nonsymmetric matrix eigenvalue problem. 1990.

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29

Rempala, Grzegorz, and Jacek Wesolowski. Symmetric Functionals on Random Matrices and Random Matchings Problems. Springer, 2010.

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30

A, Rempała Grzegorz, and Wesołowski Jacek, eds. Symmetric functionals on random matrices and random matchings problems. Springer, 2008.

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31

Symmetric Functionals on Random Matrices and Random Matchings Problems. Springer New York, 2008. http://dx.doi.org/10.1007/978-0-387-75146-7.

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32

Forrester, Peter. Wigner matrices. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.21.

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This article reviews some of the important results in the study of the eigenvalues and the eigenvectors of Wigner random matrices, that is. random Hermitian (or real symmetric) matrices with iid entries. It first provides an overview of the Wigner matrices, introduced in the 1950s by Wigner as a very simple model of random matrices to approximate generic self-adjoint operators. It then considers the global properties of the spectrum of Wigner matrices, focusing on convergence to the semicircle law, fluctuations around the semicircle law, deviations and concentration properties, and the delocal

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33

Cullum, Jane K., and Ralph A. Willoughby. Lanczos Algorithms for Large Symmetric Eigenvalue Computations Volume 1: Theory (Classics in Applied Mathematics). SIAM: Society for Industrial and Applied Mathematics, 2002.

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34

Kravtsov, Vladimir. Heavy-tailed random matrices. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.13.

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This article considers non-Gaussian random matrices consisting of random variables with heavy-tailed probability distributions. In probability theory heavy tails of distributions describe rare but violent events which usually have a dominant influence on the statistics. Furthermore, they completely change the universal properties of eigenvalues and eigenvectors of random matrices. This article focuses on the universal macroscopic properties of Wigner matrices belonging to the Lévy basin of attraction, matrices representing stable free random variables, and a class of heavy-tailed matrices obta

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35

Mann, Peter. The (Not So?) Basics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0030.

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This chapter discusses matrices. Matrices appear in many instances across physics, and it is in this chapter that the background necessary for understanding how to use them in calculations is provided. Although matrices can be a little daunting upon first exposure, they are very handy for a lot of classical physics. This chapter reviews the basics of matrices and their operations. It discusses square matrices, adjoint matrices, cofactor matrices and skew-symmetric matrices. The concepts of matrix multiplication, transpose, inverse, diagonal, identity, Pfaffian and determinant are examined. The

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36

Symmetric Functionals on Random Matrices and Random Matchings Problems (The IMA Volumes in Mathematics and its Applications Book 147). Springer, 2007.

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37

Kuijlaars, Arno. Supersymmetry. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.7.

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This article examines conceptual and structural issues related to supersymmetry. It first provides an overview of generating functions before discussing supermathematics, with a focus on Grassmann or anticommuting variables, vectors and matrices, groups and symmetric spaces, and derivatives and integrals. It then considers various applications of supersymmetry to random matrices, such as the representation of the ensemble average and the Hubbard–Stratonovich transformation, along with its generalization and superbosonization. It also describes matrix δ functions and an alternative representati

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38

Baulieu, Laurent, John Iliopoulos, and Roland Sénéor. Relativistic Wave Equations. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198788393.003.0006.

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Relativistically covariant wave equations for scalar, spinor, and vector fields. Plane wave solutions and Green’s functions. The Klein–Gordon equation. The Dirac equation and the Clifford algebra of γ‎ matrices. Symmetries and conserved currents. Hamiltonian and Lagrangian formulations. Wave equations for spin-1 fields.

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39

Harmonic Oscillators and Two-by‑two Matrices in Symmetry Problems in Physics. MDPI, 2017. http://dx.doi.org/10.3390/books978-3-03842-501-4.

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40

Newnham, Robert E. Properties of Materials. Oxford University Press, 2004. http://dx.doi.org/10.1093/oso/9780198520757.001.0001.

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Crystals are sometimes called 'Flowers of the Mineral Kingdom'. In addition to their great beauty, crystals and other textured materials are enormously useful in electronics, optics, acoustics and many other engineering applications. This richly illustrated text describes the underlying principles of crystal physics and chemistry, covering a wide range of topics and illustrating numerous applications in many fields of engineering using the most important materials today. Tensors, matrices, symmetry and structure-property relationships form the main subjects of the book. While tensors and matri

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41

Yangians and Classical Lie Algebras (Mathematical Surveys and Monographs). American Mathematical Society, 2007.

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42

Center, Langley Research, ed. Graph embedding techniques for bounding condition numbers of incomplete factor preconditioners. National Aeronautics and Space Administration, Langley Research Center, 1997.

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43

Vigdor, Steven E. Trinity. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198814825.003.0003.

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Chapter 3 explains evidence for three generations of quarks and leptons, as needed to provide natural means for standard model CP violation. It describes the cross-generational mixing of quarks and of neutrinos of different flavor, and the matrices that characterize the mixing. CP violation from quark mixing is well measured but insufficient to explain the universe’s matter–antimatter imbalance, while CP violation in neutrino mixing is the subject of ongoing searches. Discoveries revealing and quantifying flavor oscillations among neutrinos from the sun and the atmosphere are reviewed. In desc

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44

Burda, Zdzislaw, and Jerzy Jurkiewicz. Phase transitions. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.14.

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This article considers phase transitions in matrix models that are invariant under a symmetry group as well as those that occur in some matrix ensembles with preferred basis, like the Anderson transition. It first reviews the results for the simplest model with a nontrivial set of phases, the one-matrix Hermitian model with polynomial potential. It then presents a view of the several solutions of the saddle point equation. It also describes circular models and their Cayley transform to Hermitian models, along with fixed trace models. A brief overview of models with normal, chiral, Wishart, and

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45

Kostov, Ivan. String theory. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.31.

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This article discusses the link between matrix models and string theory, giving emphasis on topological string theory and the Dijkgraaf–Vafa correspondence, along with applications of this correspondence and its generalizations to supersymmetric gauge theory, enumerative geometry, and mirror symmetry. The article first provides an overview of strings and matrices, noting that the correspondence between matrix models and string theory makes it possible to solve both non-critical strings and topological strings. It then describes some basic aspects of topological strings on Calabi-Yau manifolds

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46

Akemann, Gernot, Jinho Baik, and Philippe Di Francesco, eds. The Oxford Handbook of Random Matrix Theory. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.001.0001.

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This handbook showcases the major aspects and modern applications of random matrix theory (RMT). It examines the mathematical properties and applications of random matrices and some of the reasons why RMT has been very successful and continues to enjoy great interest among physicists, mathematicians and other scientists. It also discusses methods of solving RMT, basic properties and fundamental objects in RMT, and different models and symmetry classes in RMT. Topics include the use of classical orthogonal polynomials (OP) and skew-OP to solve exactly RMT ensembles with unitary, and orthogonal

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47

Bohigas, Oriol, and Hans Weidenmuller. History – an overview. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.2.

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This article discusses the first four decades of the history of random matrix theory (RMT), that is, until about 1990. It first considers Niels Bohr's formulation of the concept of the compound nucleus, which is at the root of the use of random matrices in physics, before analysing the development of the theory of spectral fluctuations. In particular, it examines the Wishart ensemble; Dyson's classification leading to the three canonical ensembles — Gaussian Orthogonal Ensemble (GOE), Gaussian Unitary Ensemble (GUE), and Gaussian Symplectic Ensemble (GSE); and the breaking of a symmetry or an

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