Introduction to Matrix Theory (2版)

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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. Request Inspection Copy 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.

A Problem Based Journey from Elementary Number Theory to an Introduction to Matrix Theory

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Contents: Introduction Algebraic Structures The Natural Numbers The Integers The Real Numbers Introduction to Set Theory The Pigeonhole Principle and the Base 2 Number System Introduction to Group Theory Introduction to Matrix Theory Fibonacci Numbers, Determinants and Eigenvalues The Mathematics Behind Google's Page Rank and a Game of Numbers Bibliography Index Readership: High school students who love mathematics and mathematics teachers. Also good for professors of mathematics and maths education, students in the mathematical sciences and pre-service math teachers.