**Courant Lecture Notes**

2020;
569 pp;
Softcover

MSC: Primary 97; 15; 40; 20;

**Print ISBN: 978-1-4704-6160-7
Product Code: CLN/29/30**

List Price: $99.00

AMS Member Price: $79.20

MAA Member Price: $89.10

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#### Supplemental Materials

# Linear Algebra (Volumes I and II): The Set

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*Frederick P. Greenleaf; Sophie Marques*

A co-publication of the AMS and the Courant Institute of Mathematical Sciences at New York University

This is a two-volume set. Both volumes focus on linear algebra
for graduate students in mathematics, the sciences, and economics, who
have: a prior undergraduate course in the subject; a basic
understanding of matrix algebra; and some proficiency with
mathematical proofs. Proofs are emphasized and the overall objective
is to understand the structure of linear operators as the key to
solving problems in which they arise. Both volumes have been used for
several years in a one-year course sequence, Linear Algebra I and II,
offered at New York University's Courant Institute.

The first volume re-examines basic notions of linear algebra:
vector spaces, linear operators, duality, determinants,
diagonalization, and inner product spaces, giving an overview of
linear algebra with sufficient mathematical precision for advanced use
of the subject. This book provides a nice and varied selection of
exercises; examples are well-crafted and provide a clear understanding
of the methods involved. New notions are well motivated and
interdisciplinary connections are often provided, to give a more
intuitive and complete vision of linear algebra. Computational aspects
are fully covered, but the study of linear operators remains the focus
of study in this book

The first three chapters of the second volume round out the
coverage of traditional linear algebra topics: generalized
eigenspaces, further applications of Jordan form, as well as bilinear,
quadratic, and multilinear forms. The final two chapters are
different, being more or less self-contained accounts of special
topics that explore more advanced aspects of modern algebra: tensor
fields, manifolds, and vector calculus in Chapter 4 and matrix Lie
groups in Chapter 5. The reader can choose to pursue either
chapter. Both deal with vast topics in contemporary mathematics. They
include historical commentary on how modern views evolved, as well as
examples from geometry and the physical sciences in which these topics
are important.

The second volume provides a nice and varied selection of exercises;
examples are well-crafted and provide a clear understanding of the
methods involved .

Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.