31 augustus 2007

The Matrix (algebra)

If You want to delve into EEG signal analysis basics - and who would not ?- a good working knowledge of essential vector and matrix algebra is a necessity. If, like me, that knowledge is since shooltime, deeply burried somewhere into the shelves and windings of temporal cortex this very useful book will help You refresh it. It's Bronson without the movie...
In this appealing and well-written text, Richard Bronson gives readers a substructure for a firm understanding of the abstract concepts of linear algebra and its applications. The author starts with the concrete and computational, and leads the reader to a choice of major applications (Markov chains, least-squares approximation, and solution of differential equations using Jordan normal form). The first three chapters address the basics: matrices, vector spaces, and linear transformations. The next three cover eigenvalues, Euclidean inner products, and Jordan canonical forms, offering possibilities that can be tailored to the instructor's taste and to the length of the course. Bronson's approach to computation is modern and algorithmic, and his theory is clean and straightforward. Throughout, the views of the theory presented are broad and balanced. Key material is highlighted in the text and summarized at the end of each chapter. The book also includes ample exercises with answers and hints. With its inclusion of all the needed features, this text will be a pleasure for professionals, teachers, and students. Contents PREFACE, 1. MATRICES, 2. VECTOR SPACES, 3. LINEAR TRANSFORMATIONS, 4. EIGENVALUES, EIGENVECTORS, AND DIFFERENTIAL EQUATIONS, 5. EUCLIDEAN INNER PRODUCT, APPENDIX A: DETERMINANTS, APPENDIX B: JORDAN CANONICAL FORMS, APPENDIX C: MARKOV CHAINS, APPENDIX D: THE SIMPLEX METHOD, AN EXAMPLE, APPENDIX E: A WORD ON NUMERICAL TECHNIQUES AND TECHNOLOGY, ANSWERS AND HINTS TO SELECTED PROBLEMS, INDEX

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