Thomas S. Shores

Applied Linear Algebra and Matrix Analysis

• Gebundenes Buch

Produktbeschreibung

In its second edition, this textbook offers a fresh approach to matrix and linear algebra. Its blend of theory, computational exercises, and analytical writing projects is designed to highlight the interplay between these aspects of an application. This approach places special emphasis on linear algebra as an experimental science that provides tools for solving concrete problems.

The second edition's revised text discusses applications of linear algebra like graph theory and network modeling methods used in Google's PageRank algorithm. Other new materials include modeling examples of diffusive processes, linear programming, image processing, digital signal processing, and Fourier analysis. These topics are woven into the core material of Gaussian elimination and other matrix operations; eigenvalues, eigenvectors, and discrete dynamical systems; and the geometrical aspects of vector spaces.

Intended for a one-semester undergraduate course without a strict calculus prerequisite, Applied Linear Algebra and Matrix Analysis augments the key elements of linear algebra with a wide choice of optional sections. With the book's selection of applications and platform-independent assignments, instructors can tailor the curriculum to suit specific interests and ensure students across various disciplines are equipped with the powerful tools of linear algebra.

Produktdetails

• Undergraduate Texts in Mathematics
• Verlag: Springer / Springer International Publishing / Springer, Berlin
• Artikelnr. des Verlages: 978-3-319-74747-7
• 2. Aufl.
• Erscheinungstermin: 18. Mai 2018
• Englisch
• Abmessung: 241mm x 160mm x 31mm
• Gewicht: 936g
• ISBN-13: 9783319747477
• ISBN-10: 3319747479
• Artikelnr.: 50399058

Autorenporträt

Thomas S. Shores is Professor Emeritus of Mathematics at the University of Nebraska-Lincoln, where he has received awards for his teaching. His research touches on group theory, commutative algebra, mathematical modeling, numerical analysis, and inverse theory.

Inhaltsangabe

1. Linear Systems of Equations.- 2. Matrix Algebra.- 3. Vector Spaces.- 4. Geometrical Aspects of Standard Spaces.- 5. The Eigenvalue Problem.- 6. Geometrical Aspects of Abstract Spaces.

Rezensionen

"The book could be the basis of a course in matrices and linear algebra, and certainly deserves a place in a university library." (P. Macgregor, The Mathematical Gazette, Vol. 104 (560), July, 2020)

From the reviews:

"The book under review is a nice blend of three independent components of linear algebra: Theory, computation and applications. ... The book is consisting of the author preface, six chapters, table of symbols, solutions to selected exercises, a bibliography containing 13 references and subject index. ... The book is very useful for undergraduate students and nonspecialists." (Mohammad Sal Moslehian, Zentralblatt MATH, Vol. 1128 (6), 2008)

"This book is intended for a one or two semester course, with emphasis on linear algebra as an experimental science. ... The text is written in a nice conversational style. Proofs are provided for most results ... . The author also provides many computer exercises, projects, and report topics ... . Instructors wanting to encourage precision in mathematical writing will find these assignments helpful. ... This is a good text for those who want to introduce their students to applied discrete mathematics ... ." (Henry Ricardo, The Mathematical Association of America, September, 2008)