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.
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.
An Introduction to Linear Programming.
The Exterior Point Method.