This is a great book for anyone who needs to bridge the gap between traditional linear algebra and numerical linear algebra -- the no man's land of matrix analysis. While it is noted in most linear algebra texts that the set of all linear transformations on the reals, the matrices, form a linear space, not much time is spent exploring this avenue. This is unfortunate because in applications of linear algebra the objects of direct interest are matrices. One of the most important parts of matrix analysis for the applied researcher is the application of norms, and thus the construction of metric spaces, on matrix spaces. This gives one the power of calculus and the structure of linear spaces. This forms the foundation required for a good, rigorous, introduction to numerical linear algebra. This book is both deeper and broader in it's coverage than the introductions typically found in numerical linear algebra texts. While not completely rigorous, enough detail is given to allow the reader to fill in the gaps. The style is easy to follow and the organization of the work is stellar. The exercises reinforce the material. This text is appropriate for self study or as a text.
