Orthogonal Sets and Polar Methods in Linear Algebra: Applications to Matrix Calculations, Systems of Equations, Inequalities, and Linear ProgrammingISBN: 9780471328896
422 pages
February 1999

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 realworld 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, endofchapter 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.
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 realworld 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, endofchapter 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.
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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.
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.
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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.
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.
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