Further updates and revisions have been included to reflect the most up-to-date coverage of the topic, including:

• The QR algorithm for finding the eigenvalues of a self-adjoint matrix

• The Householder algorithm for turning self-adjoint matrices into tridiagonal form

• The compactness of the unit ball as a criterion of finite dimensionality of a normed linear space

Additionally, eight new appendices have been added and cover topics such as: the Fast Fourier Transform; the spectral radius theorem; the Lorentz group; the compactness criterion for finite dimensionality; the characterization of commentators; proof of Liapunov's stability criterion; the construction of the Jordan Canonical form of matrices; and Carl Pearcy's elegant proof of Halmos' conjecture about the numerical range of matrices.

Selected solutions to exercises are provided at the end of the book.

Numerous new exercises and eight new appendices have been added.