In this book we lead the student to an understanding of elementary linear algebra by emphasizing the geometric significance of the subject. Our experience in teaching beginning undergraduates over the years has convinced us that students learn the new ideas of linear algebra best when these ideas are grounded in the familiar geometry of two and three dimensions. Many important notions of linear algebra already occur in these dimensions in a non-trivial way, and a student with a confident grasp of these ideas will encounter little difficulty in extending them to higher dimensions and to more abstract algebraic systems. Moreover, we feel that this geometric approach provides a solid basis for the linear algebra needed in engineering, physics, biology, and chemistry, as well as in economics and statistics. The great advantage of beginning with a thorough study of the linear algebra of the plane is that students are introduced quickly to the most important new concepts while they are still on the familiar ground of two-dimensional geometry. In short order, the student sees and uses the notions of dot product, linear transformations, determinants, eigenvalues, and quadratic forms. This is done in Chapters 2.0-2.7. Then the very same outline is used in Chapters 3.0-3.7 to present the linear algebra of three-dimensional space, so that the former ideas are reinforced while new concepts are being introduced.

This book is a unique introduction to the theory of linear operators on Hilbert space. The authors' goal is to present the basic facts of functional analysis in a form suitable for engineers, scientists, and applied mathematicians. Although the Definition-Theorem-Proof format of mathematics is used, careful attention is given to motivation of the material covered and many illustrative examples are presented. First published in 1971, Linear Operator in Engineering and Sciences has since proved to be a popular and very useful textbook.

This book aims to be a course in Lie groups that can be covered in one year with a group of good graduate students. I have attempted to address a problem that anyone teaching this subject must have, which is that the amount of essential material is too much to cover. One approach to this problem is to emphasize the beautiful representation theory of compact groups, and indeed this book can be used for a course of this type if after Chapter 25 one skips ahead to Part III. But I did not want to omit important topics such as the Bruhat decomposition and the theory of symmetric spaces. For these subjects, compact groups are not sufficient. Part I covers standard general properties of representations of compact groups (including Lie groups and other compact groups, such as finite or p­ adic ones). These include Schur orthogonality, properties of matrix coefficients and the Peter-Weyl Theorem.

This volume examines matrix theory and its application in solving a series of problems related to natural phenomena and applied science.

Published in honor of his 70th birthday, this volume explores and celebrates the work of G.W. (Pete) Stewart, a world-renowned expert in computational linear algebra. It is widely accepted that Stewart is the successor to James Wilkinson, the first giant in the field, taking up the perturbation theory research that Wilkinson so ably began and using it as a foundation for algorithmic insights.

Several mathematical areas that have been developed independently over the last 30 years are brought together revolving around the computation of the number of integral points in suitable families of polytopes. The problem is formulated here in terms of partition functions and multivariate splines.

This text seeks to generate interest in abstract algebra by introducing each new structure and topic via a real-world application. The down-to-earth presentation is accessible to a readership with no prior knowledge of abstract algebra. Students are led to algebraic concepts and questions in a natural way through their everyday experiences.

The ADI Model Problem presents the theoretical foundations of Alternating Direction Implicit (ADI) iteration for systems with both real and complex spectra and extends early work for real spectra into the complex plane with methods for computing optimum iteration parameters for both one and two variable problems.

Dieses Buch wendet sich an aIle, die durch Neigung oder Pflicht mit der Mathematik verbunden sind: Es so11

This is the first in a series of volumes, which provide an extensive overview of conjectures and open problems in graph theory. The readership of each volume is geared toward graduate students who may be searching for research ideas. However, the well-established mathematician will find the overall exposition engaging and enlightening. Each chapter, presented in a story-telling style, includes more than a simple collection of results on a particular topic.

Designed to provide tools for independent study, this book contains student-tested mathematical exercises joined with MATLAB programming exercises.

The projectors are considered as simple but important type of matrices and operators. Their basic theory can be found in many books, among which Hal­ mas [177], [178] are of particular significance. The projectors or projections became an active research area in the last two decades due to ideas generated from linear algebra, statistics and various areas of algorithmic mathematics. There has also grown up a great and increasing number of projection meth­ ods for different purposes.