Applied Linear Algebra and Matrix Analysis

ISBN-13: 9783319747477 / Angielski / Twarda / 2018 / 479 str.

Thomas S. Shores

Opis

This text is intended as a one or two semester sophomore level course in linear algebra. It is designed to provide a balance of applications, theory and computation, and to emphasize their interdependence.

Recenzje

"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)

Spis treści

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.

O autorze

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.

Blurb

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.