This is a matrix-oriented approach to linear algebra that covers the
traditional material of the courses generally known as "Linear Algebra
I" and "Linear Algebra II" throughout North America, but it also
includes more advanced topics such as the pseudoinverse and the singular
value decomposition that make it appropriate for a more advanced course
as well. As is becoming increasingly the norm, the book begins with the
geometry of Euclidean 3-space so that important concepts like linear
combination, linear independence and span can be introduced early and in
a "real" context. The book reflects the author's background as a pure
mathematician -- all the major definitions and theorems of basic linear
algebra are covered rigorously -- but the restriction of vector spaces
to Euclidean n-space and linear transformations to matrices, for the
most part, and the continual emphasis on the system Ax=b, make the book
less abstract and more attractive to the students of today than some
others. As the subtitle suggests, however, applications play an
important role too. Coding theory and least squares are recurring
themes. Other applications include electric circuits, Markov chains,
quadratic forms and conic sections, facial recognition and computer
graphics.