# Basic Linear Algebra

Springer Science & Business Media, Jun 26, 2002 - Mathematics - 232 pages
Basic Linear Algebra is a text for first year students leading from concrete examples to abstract theorems, via tutorial-type exercises. More exercises (of the kind a student may expect in examination papers) are grouped at the end of each section. The book covers the most important basics of any first course on linear algebra, explaining the algebra of matrices with applications to analytic geometry, systems of linear equations, difference equations and complex numbers. Linear equations are treated via Hermite normal forms which provides a successful and concrete explanation of the notion of linear independence. Another important highlight is the connection between linear mappings and matrices leading to the change of basis theorem which opens the door to the notion of similarity. This new and revised edition features additional exercises and coverage of Cramer's rule (omitted from the first edition). However, it is the new, extra chapter on computer assistance that will be of particular interest to readers: this will take the form of a tutorial on the use of the "LinearAlgebra" package in MAPLE 7 and will deal with all the aspects of linear algebra developed within the book.

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### Contents

 The Algebra of Matrices 1 Some Applications of Matrices 17 Systems of Linear Equations 27 Invertible Matrices 59 Vector Spaces 69 Linear Mappings 95 The Matrix Connection 113
 Determinants 129 Eigenvalues and Eigenvectors 153 The Minimum Polynomial 175 Computer Assistance 183 Solutions to the Exercises 205 Index 231 Copyright