Orthogonal Sets and Polar Methods in Linear Algebra: Applications to Matrix Calculations, Systems of Equations, Inequalities, and Linear Programming ... Wiley Series of Texts, Monographs and Tracts) [Hardcover]

Enrique Castillo (Author), Angel Cobo (Author), Francisco Jubete (Author), Rosa Eva Pruneda (Author)

Book Description

Publication Date: February 22, 1999 | ISBN-10: 0471328898 | ISBN-13: 978-0471328896 | Edition: 1

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.

Editorial Reviews

From the Back Cover

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.

About the Author

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.

Product Details

• Hardcover: 422 pages
• Publisher: Wiley-Interscience; 1 edition (February 22, 1999)
• Language: English
• ISBN-10: 0471328898
• ISBN-13: 978-0471328896
• Product Dimensions: 9.6 x 6.4 x 1 inches
• Shipping Weight: 1.8 pounds (View shipping rates and policies)
• Average Customer Review: 4.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #3,414,173 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

4 of 4 people found the following review helpful:

4.0 out of 5 stars Good book!, February 7, 2001

By 

M. Bhardwaj "Will Read for Food" (Cambridge, MA USA.) - See all my reviews
(REAL NAME)   

This review is from: Orthogonal Sets and Polar Methods in Linear Algebra: Applications to Matrix Calculations, Systems of Equations, Inequalities, and Linear Programming ... Wiley Series of Texts, Monographs and Tracts) (Hardcover)

A linear combination of vectors allows any coefficient - positive or negative. A more powerful concept is the "cone" of a set of vectors which allows only positive combinations (more powerful because a linear space is the union of two cones, but a cone can never be expressed as a linear space). While there are many many good books on the "algebra of linear spaces" (i.e. Linear Algebra) I havent seen any that treat the "algebra of cones" with the thoroughness that this book does. I found this book useful to derive existence proofs in combinatorial optimization although the material is fundamental enough to be applied in many more fields. Best used if you have a reasonably good grasp of linear algebra.