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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.
1 Vectors in the plane and space.- 2 Vector spaces.- 3 Subspaces.- 4 Examples of vector spaces.- 5 Linear independence and dependence.- 6 Bases and finite-dimensional vector spaces.- 7 The elements of vector spaces: a summing up.- 8 Linear transformations.- 9 Linear transformations: some numerical examples.- 10 Matrices and linear transformations.- 11 Matrices.- 12 Representing linear transformations by matrices.- 12bis More on representing linear transformations by matrices.- 13 Systems of linear equations.- 14 The elements of eigenvalue and eigenvector theory.- 14bis Multilinear algebra: determinants.- 15 Inner product spaces.- 16 The spectral theorem and quadratic forms.- 17 Jordan canonical form.- 18 Applications to linear differential equations.- List of notations.