Page 10 - Advanced Linear Algebra
P. 10
xii Preface
Hilbert space theory of Chapter 13. The rather lengthy proof that every metric
space can be embedded in its completion may be omitted.
Chapter 14 contains a brief introduction to tensor products. In order to motivate
the universal property of tensor products, without getting too involved in
categorical terminology, we first treat both free vector spaces and the familiar
direct sum, in a universal way. Chapter 15 (Chapter 16 in the second edition) is
on affine geometry, emphasizing algebraic, rather than geometric, concepts.
The final chapter provides an introduction to a relatively new subject, called the
umbral calculus. This is an algebraic theory used to study certain types of
polynomial functions that play an important role in applied mathematics. We
give only a brief introduction to the subject c emphasizing the algebraic
aspects, rather than the applications. This is the first time that this subject has
appeared in a true textbook.
One final comment. Unless otherwise mentioned, omission of a proof in the text
is a tacit suggestion that the reader attempt to supply one.
Steven Roman Irvine, California
