Download or read book Linear Transformations Projection Operators and Generalized Inverses A Geometric Approach written by C. R. Rao and published by . This book was released on 1988 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: A generalized inverse of a linear transformation A: v yield w, where v and w are finite dimensional vector spaces, is defined using geometric concepts of linear transformations and projection operators. The inverse is uniquely defined in terms of specified subspaces m is a subset of v, 1 is a subset of w and a linear transformation N such that AN = O, NA = O. Such an inverse which is unique is called the 1mN-inverse. A Moore-Penrose type inverse is obtained by putting N=O. Applications to optimization problems when v and w are inner product spaces, such as least squares in a general setting, are discussed. The results given in the paper can be extended without any major modification of proofs to bounded linear operators with closed range on Hilbert spaces. Keywords: G inverse; Linear transformation; Moore Penrose inverse; Projection operator. (jhd).
Download or read book Selected Papers of C R Rao written by Calyampudi Radhakrishna Rao and published by Taylor & Francis. This book was released on 1989 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Is The Fourth Volume Of Selected Papers Of C. R. Rao Consisting Of 39 Papers Published During 1975-1985. These Papers Represent The Development Of Some Of The Basic Concepts Proposed By The Author In The Fields Of Unified Theory Of Least Squares Estimation, Weighted Distributions, Bayesian Statistical Inference, Generalised Inverses Of Matrices And Their Applications In Which Contemporary Research Is Carried Out Extensively. Work On Solutions Of Functional Equations And Their Application In Characterizations Of Distributions Is Also Of Current Interest. Introduction Of Measures Of Diversity, Quadratic Entropy And Allied Concepts Find Applications In Various Fields Such As Anthropology And Social Sciences. As In The Earlier Volumes, The Papers That Have Originally Appeared In Different Publications Have Been Retypeset To Maintain Uniformity In Presentation.The Final Volume With More Papers, An Updated Bibliography Of Works And A Comprehensive Overview Of The Total Opus Of Professor C. R. Rao Is Going To Come Out Soon.
Download or read book Generalized Inverses written by Adi Ben-Israel and published by Springer Science & Business Media. This book was released on 2006-04-18 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second edition accounts for many major developments in generalized inverses while maintaining the informal and leisurely style of the 1974 first edition. Added material includes a chapter on applications, new exercises, and an appendix on the work of E.H. Moore.
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1995 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Projection Matrices Generalized Inverse Matrices and Singular Value Decomposition written by Haruo Yanai and published by Springer Science & Business Media. This book was released on 2011-04-06 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aside from distribution theory, projections and the singular value decomposition (SVD) are the two most important concepts for understanding the basic mechanism of multivariate analysis. The former underlies the least squares estimation in regression analysis, which is essentially a projection of one subspace onto another, and the latter underlies principal component analysis, which seeks to find a subspace that captures the largest variability in the original space. This book is about projections and SVD. A thorough discussion of generalized inverse (g-inverse) matrices is also given because it is closely related to the former. The book provides systematic and in-depth accounts of these concepts from a unified viewpoint of linear transformations finite dimensional vector spaces. More specially, it shows that projection matrices (projectors) and g-inverse matrices can be defined in various ways so that a vector space is decomposed into a direct-sum of (disjoint) subspaces. Projection Matrices, Generalized Inverse Matrices, and Singular Value Decomposition will be useful for researchers, practitioners, and students in applied mathematics, statistics, engineering, behaviormetrics, and other fields.
Download or read book Contributions to Stochastics written by N. Venugopal and published by . This book was released on 1992 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Approximations to Generalized Inverses of Linear Operators written by R. H. Moore and published by . This book was released on 1973 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: For linear operators A, B on a beta-space, if B approximates A suitably then the generalized inverse of A is approximated by (B sub phi), related to but in general different from the generalized inverse of B. Applications are for numerical solutions of integral equations and approximate least squares solutions. Known matrix results are recovered. (Author).
Download or read book Generalized Inverses in Reproducing Kernel Spaces written by M. Zuhair Nashed and published by . This book was released on 1972 with total page 47 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the paper a study of generalized inverses of linear operators in reproducing kernel Hilbert spaces (RKHS) is initiated. Explicit representations of generalized inverses in RKHS are obtained, and their relations to regularization of (ill-posed or poorly-conditioned) linear operator equations are explored. It is shown in particular that this approach provides a natural and effective setting for regularization problems when the operator maps one RKHS into another. Finally properties of the regularized pseudosolutions in this setting are studied. (Author).
Download or read book Elementary Linear Algebra written by Stephen Andrilli and published by Academic Press. This book was released on 2022-04-05 with total page 546 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elementary Linear Algebra, Sixth Edition provides a solid introduction to both the computational and theoretical aspects of linear algebra, covering many important real-world applications, including graph theory, circuit theory, Markov chains, elementary coding theory, least-squares polynomials and least-squares solutions for inconsistent systems, differential equations, computer graphics and quadratic forms. In addition, many computational techniques in linear algebra are presented, including iterative methods for solving linear systems, LDU Decomposition, the Power Method for finding eigenvalues, QR Decomposition, and Singular Value Decomposition and its usefulness in digital imaging. Prepares students with a thorough coverage of the fundamentals of introductory linear algebra Presents each chapter as a coherent, organized theme, with clear explanations for each new concept Builds a foundation for math majors in the reading and writing of elementary mathematical proofs
Download or read book Proceedings of the International Conference on Linear Statistical Inference LINSTAT 93 written by Tadeusz Calinski and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: The International Conference on Linear Statistical Inference LINSTAT'93 was held in Poznan, Poland, from May 31 to June 4, 1993. The purpose of the confer ence was to enable scientists, from various countries, engaged in the diverse areas of statistical sciences and practice to meet together and exchange views and re sults related to the current research on linear statistical inference in its broadest sense. Thus, the conference programme included sessions on estimation, prediction and testing in linear models, on robustness of some relevant statistical methods, on estimation of variance components appearing in linear models, on certain gen eralizations to nonlinear models, on design and analysis of experiments, including optimality and comparison of linear experiments, and on some other topics related to linear statistical inference. Within the various sessions 22 invited papers and 37 contributed papers were presented, 12 of them as posters. The conference gathered 94 participants from eighteen countries of Europe, North America and Asia. There were 53 participants from abroad and 41 from Poland. The conference was the second of this type, devoted to linear statistical inference. The first was held in Poznan in June, 4-8, 1984. Both belong to the series of confer ences on mathematical statistics and probability theory organized under the auspices of the Committee of Mathematics of the Polish Academy of Sciences, due to the ini tiative and efforts of its Mathematical Statistics Section. In the years 1973-1993 there were held in Poland nineteen such conferences, some of them international.
Download or read book Mathematical Education written by and published by . This book was released on 1991 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Introduction to Applied Linear Algebra written by Stephen Boyd and published by Cambridge University Press. This book was released on 2018-06-07 with total page 477 pages. Available in PDF, EPUB and Kindle. Book excerpt: A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.
Download or read book KWIC Index for Numerical Algebra written by Alston Scott Householder and published by . This book was released on 1972 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Government Reports Annual Index written by and published by . This book was released on 1988 with total page 1428 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sections 1-2. Keyword Index.--Section 3. Personal author index.--Section 4. Corporate author index.-- Section 5. Contract/grant number index, NTIS order/report number index 1-E.--Section 6. NTIS order/report number index F-Z.
Download or read book Applied Linear Analysis for Chemical Engineers written by Vemuri Balakotaiah and published by Walter de Gruyter GmbH & Co KG. This book was released on 2022-12-31 with total page 784 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book details mathematical techniques for chemical and other engineers. Many practical examples encountered by chemical (and other) engineers, modern approach involving multiple length and time scales, use of symbolic software (such as Mathematica) and combination of analytical methods with graphics are included. It may be used by graduate chemical (and other) engineering students as well as industrial practitioners and possibly specialists.
Download or read book Convex Analysis and Monotone Operator Theory in Hilbert Spaces written by Heinz H. Bauschke and published by Springer Science & Business Media. This book was released on 2011-04-19 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a largely self-contained account of the main results of convex analysis and optimization in Hilbert space. A concise exposition of related constructive fixed point theory is presented, that allows for a wide range of algorithms to construct solutions to problems in optimization, equilibrium theory, monotone inclusions, variational inequalities, best approximation theory, and convex feasibility. The book is accessible to a broad audience, and reaches out in particular to applied scientists and engineers, to whom these tools have become indispensable.
Download or read book Functional Analysis and Approximation written by P.L. Butzer and published by Birkhäuser. This book was released on 2013-03-07 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: These Proceedings form a record of the lectures presented at the interna tional Conference on Functional Analysis and Approximation held at the Ober wolfach Mathematical Research Institute, August 9-16, 1980. They include 33 of the 38 invited conference papers, as well as three papers subsequently submitted in writing. Further, there is a report devoted to new and unsolved problems, based on two special sessions of the conference. The present volume is the sixth Oberwolfach Conference in Birkhauser's ISNM series to be edited at Aachen *. It is once again devoted to more significant results obtained in the wide areas of approximation theory, harmonic analysis, functional analysis, and operator theory during the past three years. Many of the papers solicited not only outline fundamental advances in their fields but also focus on interconnections between the various research areas. The papers in the present volume have been grouped into nine chapters. Chapter I, on operator theory, deals with maps on positive semidefinite opera tors, spectral bounds of semigroup operators, evolution equations of diffusion type, the spectral theory of propagators, and generalized inverses. Chapter II, on functional analysis, contains papers on modular approximation, interpolation spaces, and unconditional bases.
