"...the book is recommended for the teacher and researcher as well as for
graduate students. In fact, I think that it has a place on every mathematicians
bookshelf." (American Mathematical Monthly, November 2001)

This introduction to linear algebra by world-renowned mathematician Peter Lax
is unique in its emphasis on the analytical aspects of the subject as well as
its numerous applications. The book grew out of Dr. Lax's course notes for the
linear algebra classes he teaches at New York University. Geared to graduate
students as well as advanced undergraduates, it assumes only limited knowledge
of linear algebra and avoids subjects already heavily treated in other textbooks.
And while it discusses linear equations, matrices, determinants, and vector
spaces, it also in-cludes a number of exciting topics that are not covered
elsewhere, such as eigenvalues, the Hahn-Banach theorem, geometry, game theory,
and numerical analysis. The first four chapters are devoted to the abstract
structure of finite dimensional vector spaces. Subsequent chapters deal with
determinants as a blend of geometry, algebra, and general spectral theory.
Euclidean structure is used to explain the notion of selfadjoint mappings and
their spectral theory. Dr. Lax moves on to the calculus of vector and matrix
valued functions of a single variable.a neglected topic in most undergraduate
programs.and presents matrix inequalities from a variety of perspectives.

Fundamentals.including duality, linear mappings, and matrices

Determinant, trace, and spectral theory
Euclidean structure and the spectral theory of selfadjoint maps
Calculus of vector and matrix valued functions
Matrix inequalities
Kinematics and dynamics
Convexity and the duality theorem
Normed linear spaces, linear mappings between normed spaces, and positive
matrices
Iterative methods for solving systems of linear equations
Eight appendices devoted to important related topics, including special
determinants, Pfaff's theorem, symplectic matrices, tensor product, lattices,
fast matrix multiplication, Gershgorin's theorem, and multiplicity of eigenvalues
Later chapters cover convexity and the duality theorem, describe the basics of
normed linear spaces and linear maps between normed spaces, and discuss the
dominant eigenvalue of matrices whose entries are positive or merely non-negative.
The final chapter is devoted to numerical methods and describes Lanczos' procedure
for inverting a symmetric, positive definite matrix. Eight appendices cover
important topics that do not fit into the main thread of the book.

Clear, concise, and superbly organized, Linear Algebra is an excellent text
for advanced undergraduate and graduate courses and also serves as a handy
professional reference.

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