id: 05639410
dt: b
an: 2010c.00362
au: Ricardo, Henry
ti: A modern introduction to linear algebra.
so: Boca Raton, FL: CRC Press (ISBN 978-1-4398-0040-9/hbk). xvi, 654~p. (2010).
py: 2010
pu: Boca Raton, FL: CRC Press
la: EN
cc: H65
ut: linear algebra; textbook
ci:
li:
ab: This book is intended for a wide variety of students. Its writing style is
informal, but all definitions and results are stated precisely, the
latter with formal proofs. Concepts and results are motivated and
introduced by explanations and worked examples and, in fact, one of the
strong points of this book is the number of worked examples. The
approach is via vectors in ${\bbfR}^n$ and matrices; these are treated
in Chapter 1, along with linear independence, bases and subspaces.
Chapter 2 deals thoroughly with systems of equations and Gaussian
elimination. Chapter 3 is on matrix algebra, matrix-vector
multiplication and the inverse matrix. Chapter 4 deals with
eigenvalues, eigenvectors and diagonalization. The determinant of a
square matrix $A$ is defined in terms of the $PA=LU$ factorization. The
Cayley-Hamilton theorem is proved for diagonalizable matrices and the
minimal polynomial is introduced. Chapter 5 treats vector spaces
abstractly, Chapter 6 covers linear transformations, Chapter 7 treats
real and complex inner product spaces, the Gram-Schmidt process, and
the Schur and QR factorizations. Finally, Chapter 8 deals with
hermitian and normal matrices and quadratic forms, and concludes with
the singular value and polar decompositions. Many applications of
linear algebra are introduced in the text and in examples and the many
exercises. There are over 1200 of the latter, and they are classified
according to difficulty. Attention is also drawn to the use of
calculators and computers where relevant. A very useful feature of the
book is that each chapter ends with a summary of key definitions and
results. The book contains answers or hints to the odd-numbered
exercises and an instructorâ€™s solutions manual is forthcoming.
rv: Rabe von Randow (Bonn)