Basic Linear Algebra

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Springer Science & Business Media, Jun 26, 2002 - 232 pages
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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
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