Linear Algebra

Author: Fuzhen Zhang
Publisher: JHU Press
ISBN: 9780801854590
Format: PDF, Kindle
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"Linear algebra is an increasingly important part of any curriculum in mathematics in our days... A well-organized problem book, like this, will surely be welcomed by students as well as by instructors." -- Zentralblatt fuer Mathematik

Matrix Computations

Author: Gene H. Golub
Publisher: JHU Press
ISBN: 1421407949
Format: PDF, ePub
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The fourth edition of Gene H. Golub and Charles F. Van Loan's classic is an essential reference for computational scientists and engineers in addition to researchers in the numerical linear algebra community. Anyone whose work requires the solution to a matrix problem and an appreciation of its mathematical properties will find this book to be an indispensible tool. This revision is a cover-to-cover expansion and renovation of the third edition. It now includes an introduction to tensor computations and brand new sections on • fast transforms• parallel LU• discrete Poisson solvers• pseudospectra• structured linear equation problems• structured eigenvalue problems• large-scale SVD methods• polynomial eigenvalue problems Matrix Computations is packed with challenging problems, insightful derivations, and pointers to the literature—everything needed to become a matrix-savvy developer of numerical methods and software.

Applied Numerical Linear Algebra

Author: James W. Demmel
Publisher: SIAM
ISBN: 0898713897
Format: PDF, Docs
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This comprehensive textbook is designed for first-year graduate students from a variety of engineering and scientific disciplines.

Numerical Linear Algebra

Author: Lloyd N. Trefethen
Publisher: SIAM
ISBN: 9780898719574
Format: PDF, ePub
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A concise, insightful, and elegant introduction to the field of numerical linear algebra. Designed for use as a stand-alone textbook in a one-semester, graduate-level course in the topic, it has already been class-tested by MIT and Cornell graduate students from all fields of mathematics, engineering, and the physical sciences. The authors' clear, inviting style and evident love of the field, along with their eloquent presentation of the most fundamental ideas in numerical linear algebra, make it popular with teachers and students alike.

Numerical Linear Algebra for Applications in Statistics

Author: James E. Gentle
Publisher: Springer Science & Business Media
ISBN: 1461206235
Format: PDF, ePub, Docs
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Accurate and efficient computer algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors. Regardless of the software system used, the book describes and gives examples of the use of modern computer software for numerical linear algebra. It begins with a discussion of the basics of numerical computations, and then describes the relevant properties of matrix inverses, factorisations, matrix and vector norms, and other topics in linear algebra. The book is essentially self- contained, with the topics addressed constituting the essential material for an introductory course in statistical computing. Numerous exercises allow the text to be used for a first course in statistical computing or as supplementary text for various courses that emphasise computations.

A terse Introduction to Linear Algebra

Author: Yitzhak Katznelson
Publisher: American Mathematical Soc.
ISBN: 0821844199
Format: PDF
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Linear algebra is the study of vector spaces and the linear maps between them. It underlies much of modern mathematics and is widely used in applications. A (Terse) Introduction to Linear Algebra is a concise presentation of the core material of the subject--those elements of linear algebra that every mathematician, and everyone who uses mathematics, should know. It goes from the notion of a finite-dimensional vector space to the canonical forms of linear operators and their matrices, and covers along the way such key topics as: systems of linear equations, linear operators and matrices, determinants, duality, and the spectral theory of operators on inner-product spaces. The last chapter offers a selection of additional topics indicating directions in which the core material can be applied. The Appendix provides all the relevant background material. Written for students with some mathematical maturity and an interest in abstraction and formal reasoning, the book is self-contained and is appropriate for an advanced undergraduate course in linear algebra.

The Chinese Roots of Linear Algebra

Author: Roger Hart
Publisher: JHU Press
ISBN: 9780801899584
Format: PDF, Mobi
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Mathematicians and historians of mathematics and science will find in The Chinese Roots of Linear Algebra new ways to conceptualize the intellectual development of linear algebra.

Linear Algebra Problem Book

Author: Paul R. Halmos
Publisher: MAA
ISBN: 9780883853221
Format: PDF, ePub
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Takes the student step by step from basic axioms to advanced concepts. 164 problems, each with hints and full solutions.

Matrices Moments and Quadrature with Applications

Author: Gene H. Golub
Publisher: Princeton University Press
ISBN: 9781400833887
Format: PDF, ePub, Mobi
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This computationally oriented book describes and explains the mathematical relationships among matrices, moments, orthogonal polynomials, quadrature rules, and the Lanczos and conjugate gradient algorithms. The book bridges different mathematical areas to obtain algorithms to estimate bilinear forms involving two vectors and a function of the matrix. The first part of the book provides the necessary mathematical background and explains the theory. The second part describes the applications and gives numerical examples of the algorithms and techniques developed in the first part. Applications addressed in the book include computing elements of functions of matrices; obtaining estimates of the error norm in iterative methods for solving linear systems and computing parameters in least squares and total least squares; and solving ill-posed problems using Tikhonov regularization. This book will interest researchers in numerical linear algebra and matrix computations, as well as scientists and engineers working on problems involving computation of bilinear forms.

Problems and Theorems in Linear Algebra

Author: Viktor Vasil_evich Prasolov
Publisher: American Mathematical Soc.
ISBN: 0821802364
Format: PDF, ePub, Mobi
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There are a number of very good books available on linear algebra. However, new results in linear algebra appear constantly, as do new, simpler, and better proofs of old results. Many of these results and proofs obtained in the past thirty years are accessible to undergraduate mathematics majors, but are usually ignored by textbooks. In addition, more than a few interesting old results are not covered in many books. In this book, the author provides the basics of linear algebra, with an emphasis on new results and on nonstandard and interesting proofs. The book features about 230 problems with complete solutions. It can serve as a supplementary text for an undergraduate or graduate algebra course.