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This is a graduate textbook covering an especially broad range of topics. The first part of the book contains a careful but rapid discussion of the basics of linear algebra, including vector spaces, linear transformations, quotient spaces, and isomorphism theorems. The author then proceeds to modules, emphasizing a comparison with vector spaces. A thorough discussion of inner product spaces, eigenvalues, eigenvectors, and finite dimensional spectral theory follows, culminating in the finite dimensional spectral theorem for normal operators. The second part of the book is a collection of topics, including metric vector spaces, metric spaces, Hilbert spaces, tensor products, and affine geometry. The last chapter discusses the umbral calculus, an area of modern algebra with many important applications. The new edition has been thoroughly rewritten, both in the text and exercise sets, and contains new chapters on convexity and separation, positive solutions to linear systems, singular values and QR decompostion. Treatments of tensor products and the umbral calculus have been greatly expanded and discussions of determinants, complexification of a real vector space, Schur's lemma and Gersgorin disks have been added. The author is Emeritus Professor of Mathematics, having taught at a number of universities, including MIT, UC Santa Barabara, the University of South Florida, the California State University at Fullerton and UC Irvine. He has written 27 books in mathematics at various levels and 9 books on computing. His interests lie mostly in the areas of algebra, set theory and logic, probability and finance.

Algebras, Linear. --- Linear algebra --- Algebra, Universal --- Generalized spaces --- Mathematical analysis --- Calculus of operations --- Line geometry --- Topology --- Matrix theory. --- Linear and Multilinear Algebras, Matrix Theory. --- Algebra. --- Mathematics

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Algebras, Linear. --- Algèbre linéaire --- Algebras, Linear --- 512.64 --- 512.64 Linear and multilinear algebra. Matrix theory --- Linear and multilinear algebra. Matrix theory --- Linear algebra --- Algebra, Universal --- Generalized spaces --- Mathematical analysis --- Calculus of operations --- Line geometry --- Topology --- Algèbre linéaire

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This book presents the author’s new method of two-stage maximization of likelihood function, which helps to solve a series of non-solving before the well-posed and ill-posed problems of pseudosolution computing systems of linear algebraic equations (or, in statistical terminology, parameters’ estimators of functional relationships) and linear integral equations in the presence of deterministic and random errors in the initial data. This book, for the first time, presents a solution of the problem of reciprocal influence of passive errors of regressors and of active errors of predictors by computing point estimators of functional relationships. Audience This book is intended for students, postgraduate students, scientists, and other researchers on handling economical and technical data. The book is especially intended for those who constantly use regression analysis in their own research and for those who create the mathematical software for computers.

Functional equations. --- Algebras, Linear. --- Linear algebra --- Algebra, Universal --- Generalized spaces --- Mathematical analysis --- Calculus of operations --- Line geometry --- Topology --- Equations, Functional --- Functional analysis --- Computer science --- Econometrics. --- Computational Mathematics and Numerical Analysis. --- Mathematics. --- Economics, Mathematical --- Statistics --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Mathematics --- Computer mathematics.

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This book is dedicated to relatively recent results in linear algebra with indefinite inner product. It also includes applications to differential and difference equations with symmetries, matrix polynomials and Riccati equations. These applications have been developed in the last fifty years, and all of them are based on linear algebra in spaces with indefinite inner product. The latter forms a new more or less independent branch of linear algebra and we gave it the name of indefinite linear algebra. This new subject in linear algebra is presented following the lines and principles of a standard linear algebra course. This book has the structure of a graduate text in which chapters of advanced linear algebra form the core. This together with the many significant applications and accessible style will make it widely useful for engineers, scientists and mathematicians alike.

Functions of several complex variables. --- Analytic spaces. --- Indefinite inner product spaces. --- Algebras, Linear. --- Linear algebra --- Algebra, Universal --- Generalized spaces --- Mathematical analysis --- Calculus of operations --- Line geometry --- Topology --- Indefinite scalar product spaces --- Inner product spaces, Indefinite --- Scalar product spaces, Indefinite --- Spaces with indefinite inner product --- Inner product spaces --- Spaces, Analytic --- Analytic functions --- Functions of several complex variables --- Complex variables --- Several complex variables, Functions of --- Functions of complex variables --- Operator theory. --- Matrix theory. --- Differential Equations. --- Operator Theory. --- Linear and Multilinear Algebras, Matrix Theory. --- Ordinary Differential Equations. --- 517.91 Differential equations --- Differential equations --- Functional analysis --- Analytic spaces --- Indefinite inner product spaces --- Algebras, Linear --- Algebra. --- Differential equations. --- Mathematics