INVARIANT SUBSPACES OF MATRICES WITH APPLICATIONS: (Second Edition)

by Israel Gohberg, Peter Lancaster, and Leiba Rodman
SIAM Classics in Applied Mathematics, 2006. 692 pages.


INDEFINITE LINEAR ALGEBRA WITH APPLICATIONS

by Israel Gohberg, Peter Lancaster, and Leiba Rodman
Birkhauser, Basel, 2005. 357 pages.
ISBN 3-7643-7349-0

This book is written for graduate students, engineers, scientists and mathematicians. It starts with the theory of subspaces and orthogonalization and then goes on to the theory of matrices, perturbation and stability theory. All of this material is developed in the context of linear spaces with an indefinite inner product. The book also includes applications of the theory to the study of matrix polynomials with selfadjoint coefficients, to differential and difference equations (of first and higher order) with constant coefficients, and to algebraic Riccati equations.


LAMBDA-MATRICES AND VIBRATING SYSTEMS: (Second Edition)

by Peter Lancaster
Dover, Mineola, 2002. 193 pages.>br> ISBN 0-486-42546-0

(From the preface to the first edition:)

The author's primary purpose in writing this book is to present under one cover several aspects and solutions of the problems of linear vibrating systems with a finite number of degrees of freedom, together with a careful account of that part of the theory of matrices required to deal with these problems efficiently. The treatment is intended to be mathematically sound and yet involve the reader in a minimum of mathematical abstraction. The results of the later chapters are then more readily available to those engaged in the practical analysis of vibrating systems. Indeed, the reader may prefer to dip straight into the later chapters on applications and refer back to the first four chapters for enlargement on theoretical issues as this becomes necessary.


TRANSFORM METHODS IN APPLIED MATHEMATICS: AN INTRODUCTION

by Peter Lancaster and Kestutis Salkauskas
John Wiley, New York, 1996. 332 pages.
ISBN 0-471-00810-9

This book contains an introductory course of study in the theory and practice of continuous and discrete transforms. It developed from a course given by the authors over several years which was required for geophysics majors. The most unusual feature is the presentation of what is generally seen as advanced material at a third-year undergraduate level. In order to provide users with an early introduction to important techniques, and to give math majors an early introduction to the same topics, heuristic argument and discussion are combined with careful mathematical statements.
In order to make the book accessible to a variety of audiences there are five appendices giving careful reviews of necessary topics from algebra and calculus.


ALGEBRAIC RICCATI EQUATIONS

by Peter Lancaster and Leiba Rodman
Oxford University Press, 1995. 480 pages.
ISBN 0-19-853795-6

In this monograph we make a self-contained survey of the available knowledge (at the time of writing) of the nature of the solution sets of algebraic Riccati equations (ARE) of the two principal types (CARE and DARE). The book is in four parts:

PART I - MATRIX THEORY. PART II - CONTINUOUS ALGEBRAIC RICCATI EQUATIONS. PART III - DISCRETE ALGEBRAIC RICCATI EQUATIONS. PART IV - APPLICATIONS AND CONNECTIONS


Lectures on LINEAR ALGEBRA, CONTROL, AND STABILITY

by Peter Lancaster with Dan Veiner
Department of mathematics and Statistics, University of Calgary, 1999. 72 pages.

Chapter 1: Basic Materials
Chapter 2: Stability and Canonical Forms
Chapter 3: Realization of Rational Matrix Functions
Chapter 4: Balanced Realization and Model Reduction
Chapter 5: Algebraic Riccati Equations for Continuous Systems
Chapter 6: Algebraic Riccati Equations for Continuous Systems
Chapter 7: Stability
REFERENCES