Linear algebra and matrix theory are essentially synonymous terms for an
area of mathematics that has become one of the most useful and pervasive
tools in a wide range of disciplines. It is also a subject of great
mathematical beauty. In consequence of both of these facts, linear
algebra has increasingly been brought into lower levels of the
curriculum, either in conjunction with the calculus or separate from it
but at the same level. A large and still growing number of textbooks has
been written to satisfy this need, aimed at students at the junior,
sophomore, or even freshman levels. Thus, most students now obtaining a
bachelor's degree in the sciences or engineering have had some exposure
to linear algebra. But rarely, even when solid courses are taken at the
junior or senior levels, do these students have an adequate working
knowledge of the subject to be useful in graduate work or in research
and development activities in government and industry. In particular,
most elementary courses stop at the point of canonical forms, so that
while the student may have "seen" the Jordan and other canonical forms,
there is usually little appreciation of their usefulness. And there is
almost never time in the elementary courses to deal with more
specialized topics like nonnegative matrices, inertia theorems, and so
on. In consequence, many graduate courses in mathematics, applied mathe-
matics, or applications develop certain parts of matrix theory as
needed.