Linear algebra and matrix theory are among the most important and most frequently applied branches of mathematics. They are especially important in solving engineering and economic models, where either the model is assumed linear, or the nonlinear model is approximated by a linear model, and the resulting linear model is examined.
This book is mainly a textbook, that covers a one semester upper division course or a two semester lower division course on the subject.
The second edition will be an extended and modernized version of the first edition. We added some new theoretical topics and some new applications from fields other than economics. We also added more difficult exercises at the end of each chapter which require deep understanding of the theoretical issues. We also modernized some proofs in the theoretical discussions which give better overview of the study material. In preparing the manuscript we also corrected the typos and errors, so the second edition will be a corrected, extended and modernized new version of the first edition.
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Sample Chapter(s)
Preface
Chapter 1: Vectors and Matrices
Contents:
- Vectors and Matrices
- Vector Spaces and Inner-Product Spaces
- Systems of Linear Equations, and Inverses of Matrices
- Determinants
- Linear Mappings and Matrices
- Eigenvalues, Invariant Subspaces, Canonical Forms
- Special Matrices
- Elements of Matrix Analysis
Readership: Written primarily for undergraduate and graduate students studying engineering, economics and business; can also be used in courses offered by the mathematics department, or by any kind of engineering and social sciences; can also be used by researchers in mathematics, economics, engineering; in addition, high school special courses, and teacher training courses can employ this textbook.
Prof. Ferenc Szidarovszky is a mathematician focusing mainly on game theory, control and system theory, dynamic systems with applications to engineering and economics, numerical analysis and computation, optimization, operations research, calculus and their applications in economic sciences, linear algebra.
He was an invited lecturer at the Delft University, Groningen University, Rutgers University, Princeton University, University of Technology, Sydney, University of Melbourne. He was a full professor at the Department of Systems and Industrial Engineering of the University of Arizona between 1998 and 2011 and was visiting professor at the University of Texas at El Paso, University of Technology, Sydney, and at Chuo University, Tokyo. He was an invited lecturer at many institutions all over the world.
Prof. Sandor Molnar is a mathematician specialising in control and systems theory with a special focus on linear systems and applied mathematics in energy systems modeling. He is currently giving lectures as a professor emeritus at Szent Istvan University. He was an invited lecturer at the Chicago University, the University of Arizona, the Tokyo Metropolitan University and the Barcelona Technical University. He gives lectures in linear algebra, applications of control and systems theory, computational theory and energy modeling.
Dr Mark Molnar is an economist, currently an associate professor at ELTE- Eötvös Lóránd University of Sciences, Faculty of Economics. Previously he was a Head of Department of Macroeconomics and International Economics at Szent Istvan University. He has given lectures in micro and macroeconomics, applied economics, international economics, linear algebra, calculus, dynamic systems and time series analysis. His research encompasses energy systems and climate change emissions modelling, artificial neural networks and time series analysis.