Linear Algebra

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Springer Science & Business Media, Dec 6, 2012 - Mathematics - 364 pages
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In the second edition of this popular and successful text the number of exercises has been drastically increased (to a minimum of 25 per chapter); also a new chapter on the Jordan normal form has been added. These changes do not affect the character of the book as a compact but mathematically clean introduction to linear algebra with particular emphasis on topics that are used in the theory of differential equations.
 

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Contents

Vectors in the plane and space
1
Vector spaces
13
Subspaces
21
Examples of vector spaces
27
Linear independence and dependence
35
Bases and finitedimensional vector spaces
42
a summing up
56
Linear transformations
65
Representing linear transformations by matrices
130
12bis More on representing linear transformations by matrices
153
Systems of linear equations
165
The elements of eigenvalue and eigenvector theory
191
determinants
225
Inner product spaces
244
The spectral theorem and quadratic forms
274
Jordan canonical form
303

some numerical examples
90
Matrices and linear transformations
104
Matrices
112
Applications to linear differential equations
334
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