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.Content:
Chapter 1 Basic Concepts (pages 1–22):
Chapter 2 Orthogonal Sets (pages 23–40):
Chapter 3 Matrix Calculations Using Orthogonal Sets (pages 41–72):
Chapter 4 More Applications of Orthogonal Sets (pages 73–84):
Chapter 5 Orthogonal Sets and Systems of Linear Equations (pages 85–142):
Chapter 6 Polyhedral Convex Cones (pages 143–190):
Chapter 7 Polytopes and Polyhedra (pages 191–213):
Chapter 8 Cones and Systems of Inequalities (pages 215–250):
Chapter 9 An Introduction to Linear Programming (pages 251–274):
Chapter 10 The Exterior Point Method (pages 275–341):
Chapter 11 Applications (pages 343–391):
