Linear Algebra

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.