Orthogonal Sets and Polar Methods in Linear Algebra: Applications to Matrix Calculations, Systems of Equations, Inequalities, and Linear Programming

ISBN-13: 9780471328896 / Angielski / Twarda / 1999 / 440 str.

Enrique del Castillo; Enrique Castillo; Angel Cobo

Opis

A first-year graduate text on linear algebra for applications, this book is divided into four parts. The first part deals with linear spaces, matrices, systems of equations (including the problems of compatibility and uniqueness), and obtaining their solutions. The second part deals with cones and systems of linear equalities and inequalities in unrestricted, restricted and strictly restricted variables. The third part presents linear programming problems and the new exterior-point method. The fourth presents a wide collection of examples from the areas of mathematics, physics, and engineering, such as the matrix analysis of structures, input-output tables, and diet and network flow problems. All models presented are taken from real-life problems.

Spis treści

LINEAR SPACES AND SYSTEMS OF EQUATIONS.

Basic Concepts.

Orthogonal Sets.

Matrix Calculations Using Orthogonal Sets.

More Applications of Orthogonal Sets.

Orthogonal Sets and Systems of Linear Equations.

CONES AND SYSTEMS OF INEQUALITIES.

Polyhedral Convex Cones.

Polytopes and Polyhedra.

Cones and Systems of Inequalities.

LINEAR PROGRAMMING.

An Introduction to Linear Programming.

The Exterior Point Method.

APPLICATIONS.

Applications.

Appendices.

References.

Index.

O autorze

ENRIQUE CASTILLO is a professor in the Department of Applied Mathematics and Computational Science at the University of Cantabria, Spain. During 25 years of research and teaching, he has published hundreds of papers as well as 18 books. ANGEL COBO is an associate professor in the Department of Applied Mathematics and Computational Science in the University of Cantabria.

FRANCISCO JUBETE is a civil engineer and research assistant in the Department of Applied Mathematics and Computational Science at the University of Cantabria.

ROSA EVA PRUNEDA is a research assistant in the Department of Applied Mathematics and Computational Sciences at the University of Cantabria.

Blurb

A unique, applied approach to problem solving in linear algebra

Departing from the standard methods of analysis, this unique book presents methodologies and algorithms based on the concept of orthogonality and demonstrates their application to both standard and novel problems in linear algebra. Covering basic theory of linear systems, linear inequalities, and linear programming, it focuses on elegant, computationally simple solutions to real–world physical, economic, and engineering problems. The authors clearly explain the reasons behind the analysis of different structures and concepts and use numerous illustrative examples to correlate the mathematical models to the reality they represent. Readers are given precise guidelines for:
∗ Checking the equivalence of two systems
∗ Solving a system in certain selected variables
∗ Modifying systems of equations
∗ Solving linear systems of inequalities
∗ Using the new exterior point method
∗ Modifying a linear programming problem

With few prerequisites, but with plenty of figures and tables, end–of–chapter exercises as well as Java and Mathematica programs available from the authors′ Web site, this is an invaluable text/reference for mathematicians, engineers, applied scientists, and graduate students in mathematics.