Linear Algebra for the 21st Century

Description

Linear Algebra for 21st Century Applications adapts linear algebra to best suit modern teaching and application, and it places SVD as central to the text early on to empower the students in these disciplines to learn and use the best techniques.

• Reforms linear algebra to best suit 21st century teaching, theory and application
• The Singular Value Decomposition (SVD) is a key enabling tool sometimes called the jewel in the crown of linear algebra but this book utilises its power for both applications and theory in a world of ubiquitous computing

About the Author(s)

Anthony Roberts, Professor of Applied Mathematics, University of Adelaide

A. J. Roberts is a Professor and Chair in the School of Mathematical Sciences at the University of Adelaide. He is a leader in developing and applying a branch of modern dynamical systems theory to understand the relation between detailed microscale models and average macroscale models. In conjunction with new computer algebra algorithms in scientific computing, Professor Roberts derives and interprets mathematical and computational models of complex multiscale systems, both deterministic and stochastic. He develops applications of this methodology to free surface fluid dynamics in the flow of thin fluid layers, water waves, and on to turbulent floods and tsunamis. His research programs have been supported by a dozen large research grants from the Australian Research Council.

Table of Contents

1:Vectors
2:Systems of linear equations
3:Matrices encode system interactions
4:Eigenvalues and eigenvectors of symmetric matrices
5:Approximate matrices
6:Determinants distinguish matrices
7:Eigenvalues and eigenvectors in general

Reviews

"Highly recommended for everyone needing linear algebra competence and looking for a motivating, application oriented, comprehensible yet complete text, using modern computational tools." - Dieter Riebesehl, zbMATH Open

"this is the first text I have read that uses SVD as the main operation to solve systems of linear equations instead of the traditional augmented matrix and elementary row operations to obtain a reduced row echelon form" - Peter Olszewski, Pennsylvania State University, Acta Crystallographica