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Books on the topic 'Singularna matrica'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Kei, Takeuchi, Takane Yoshio, and SpringerLink (Online service), eds. Projection Matrices, Generalized Inverse Matrices, and Singular Value Decomposition. Springer Science+Business Media, LLC, 2011.

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2

Yanai, Haruo, Kei Takeuchi, and Yoshio Takane. Projection Matrices, Generalized Inverse Matrices, and Singular Value Decomposition. Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4419-9887-3.

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3

Böttcher, Albrecht, Israel Gohberg, and Peter Junghanns, eds. Toeplitz Matrices and Singular Integral Equations. Birkhäuser Basel, 2002. http://dx.doi.org/10.1007/978-3-0348-8199-9.

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4

Wei, Li. A singular loop transformation framework based on non-singular matrices. Cornell Theory Center, Cornell University, 1992.

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5

Demmel, J. W. On computing accurate singular values and eigenvalues of acyclic matrices. Naval Postgraduate School, 1992.

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6

Demmel, James. Computing small singular values of bidiagonal matrices with guaranteed high relative accuracy. Courant Institute of Mathematical Sciences, New York University, 1988.

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7

Sezginer, R. The largest singular value of e{sup}x A{sub}o e -x is convex on convex sets of commuting matrices. Courant Institute of Mathematical Sciences, New York University, 1988.

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8

Bouchaud, Jean-Phillipe, and Marc Potters. Asymptotic singular value distributions in information theory. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.41.

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This article examines asymptotic singular value distributions in information theory, with particular emphasis on some of the main applications of random matrices to the capacity of communication channels. Results on the spectrum of random matrices have been adopted in information theory. Furthermore, information theorists, motivated by certain channel models, have obtained a number of new results in random matrix theory (RMT). Most of those results are related to the asymptotic distribution of the (square of) the singular values of certain random matrices that model data communication channels

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9

Takeuchi, Kei, Haruo Yanai, and Yoshio Takane. Projection Matrices, Generalized Inverse Matrices, and Singular Value Decomposition. Springer, 2011.

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10

Zabrodin, Anton. Financial applications of random matrix theory: a short review. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.40.

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This article reviews some applications of random matrix theory (RMT) in the context of financial markets and econometric models, with emphasis on various theoretical results (for example, the Marčenko-Pastur spectrum and its various generalizations, random singular value decomposition, free matrices, largest eigenvalue statistics) as well as some concrete applications to portfolio optimization and out-of-sample risk estimation. The discussion begins with an overview of principal component analysis (PCA) of the correlation matrix, followed by an analysis of return statistics and portfolio theor

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11

Bouchaud, Jean-Philippe. Random matrix theory and (big) data analysis. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198797319.003.0006.

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This chapter reviews methods from random matrix theory to extract information about a large signal matrix C (for example, a correlation matrix arising in big data problems), from its noisy observation matrix M. The chapter shows that the replica method can be used to obtain both the spectral density and the overlaps between noise-corrupted eigenvectors and the true ones, for both additive and multiplicative noise. This allows one to construct optimal rotationally invariant estimators of C based on the observation of M alone. This chapter also discusses the case of rectangular correlation matri

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12

1941-, Silbermann Bernd, Böttcher Albrecht, Gohberg I. 1928-, and Junghanns Peter 1953-, eds. Toeplitz matrices and singular integral equations: The Bernd Silbermann anniversary volume. Birkhauser Verlag, 2002.

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13

Adler, Mark. Universality. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.6.

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This article deals with the universality of eigenvalue spacings, one of the basic characteristics of random matrices. It first discusses the heuristic meaning of universality before describing the standard universality classes (sine, Airy, Bessel) and their appearance in unitary, orthogonal, and symplectic ensembles. It then examines unitary matrix ensembles in more detail and shows that universality in these ensembles comes down to the convergence of the properly scaled eigenvalue correlation kernels. It also analyses the Riemann–Hilbert method, along with certain non-standard universality cl

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14

Factorization of Matrix Functions and Singular Integral Operators. Birkhäuser, 2013.

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15

Toeplitz Matrices and Singular Integral Equations: The Bernd Silbermann Anniversary Volume (Operator Theory, Advances and Applications, V. 135.). Birkhauser, 2002.

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16

Barel, Marc Van, Raf Vandebril, and Nicola Mastronardi. Matrix Computations and Semiseparable Matrices Vol. 2: Eigenvalue and Singular Value Methods. Johns Hopkins University Press, 2008.

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17

Chimenti, Dale, Stanislav Rokhlin, and Peter Nagy. Physical Ultrasonics of Composites. Oxford University Press, 2011. http://dx.doi.org/10.1093/oso/9780195079609.001.0001.

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Physical Ultrasonics of Composites is a rigorous introduction to the characterization of composite materials by means of ultrasonic waves. Composites are treated here not simply as uniform media, but as inhomogeneous layered anisotropic media with internal structure characteristic of composite laminates. The objective here is to concentrate on exposing the singular behavior of ultrasonic waves as they interact with layered, anisotropic materials, materials which incorporate those structural elements typical of composite laminates. This book provides a synergistic description of both modeling a

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18

Cheng, Russell. The Skew Normal Distribution. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198505044.003.0012.

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This chapter considers the univariate skew-normal distribution, a generalization of the normal that includes the normal as a special case. The most natural parametrization is non-standard. This is because the Fisher information matrix is then singular at the true parameter value when the true model is the normal special case. The log-likelihood is then particularly flat in a certain coordinate direction. Standard theory cannot then be used to calculate the asymptotic distribution of all the parameter estimates. This problem can be handled using an alternative parametrization. There is another

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19

Bennister, Mark, Ben Worthy, and Paul 't Hart, eds. The Leadership Capital Index. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198783848.001.0001.

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This edited book will make an important, timely, and innovative contribution to the now flourishing academic discipline of political leadership studies. We have developed a conceptual framework of leadership capital and a diagnostic tool—the Leadership Capital Index (LCI)—to measure and evaluate the fluctuating nature of leadership capital. Differing amounts of leadership capital, a combination of skills, relations, and reputation, allow leaders to succeed or fail. This book brings together leading international scholars to engage with the concept of “leadership capital” and apply the LCI to a

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