This little collection of poems, stories, outbursts and musings is put forward as an homage to Jerome K. Jerome. His book, Idle Thoughts of an Idle Fellow, published in 1886, is like mine, a series of humorous articles on various subjects.

Have you ever experienced a strong compulsion to head for the hills? In your dreams have you ever pictured yourself running free over some beautiful moorland landscape, with the wind in your hair and the heather tickling you elsewhere? Perhaps, until now, you have put it down to eating cheese before going to bed? Well, maybe it is the Call of the North - inviting you to explore the Pennines. Maybe it is time to set aside life's problems, step into the footprints of the heroes of old and lose yourself in some exquisite wilderness. Join Peter Lancaster as he dodges death and disaster travelling the Pennines, with only 'Auntie' (his 1963 Rover) for company...apart from his wife Jane, sheepdog and pint of beer. When life is an uphill struggle, why not pause and take a look at the view for a while?

This book provides a careful treatment of the theory of algebraic Riccati equations. It consists of four parts: the first part is a comprehensive account of necessary background material in matrix theory including careful accounts of recent developments involving indefinite scalar products and rational matrix functions. The second and third parts form the core of the book and concern the solutions of algebraic Riccati equations arising from continuous and discrete systems. The geometric theory and iterative analysis are both developed in detail. The last part of the book is an exciting collection of eight problem areas in which algebraic Riccati equations play a crucial role. These applications range from introductions to the classical linear quadratic regulator problems and the discrete Kalman filter to modern developments in HD*W*w control and total least squares methods.

This book is dedicated to the memory of Israel Gohberg (1928-2009) - one of the great mathematicians of our time - who inspired innumerable fellow mathematicians and directed many students. The volume reflects the wide spectrum of Gohberg's mathematical interests. It consists of more than 25 invited and peer-reviewed original research papers written by his former students, co-authors and friends. Included are contributions to single and multivariable operator theory, commutative and non-commutative Banach algebra theory, the theory of matrix polynomials and analytic vector-valued functions, several variable complex function theory, and the theory of structured matrices and operators. Also treated are canonical differential systems, interpolation, completion and extension problems, numerical linear algebra and mathematical systems theory.

In this article we shall use two special classes of reproducing kernel Hilbert spaces (which originate in the work of de Branges [dB) and de Branges-Rovnyak [dBRl), respectively) to solve matrix versions of a number of classical interpolation problems. Enroute we shall reinterpret de Branges' characterization of the first of these spaces, when it is finite dimensional, in terms of matrix equations of the Liapunov and Stein type and shall subsequently draw some general conclusions on rational m x m matrix valued functions which are "J unitary" a.e. on either the circle or the line. We shall also make some connections with the notation of displacement rank which has been introduced and extensively studied by Kailath and a number of his colleagues as well as the one used by Heinig and Rost [HR). The first of the two classes of spaces alluded to above is distinguished by a reproducing kernel of the special form K (>.) = J - U(>')JU(w)* (Ll) w Pw(>') , in which J is a constant m x m signature matrix and U is an m x m J inner matrix valued function over ~+, where ~+ is equal to either the open unit disc ID or the open upper half plane (1)+ and Pw(>') is defined in the table below.

R. S. PHILLIPS I am very gratified to have been asked to give this introductory talk for our honoured guest, Israel Gohberg. I should like to begin by spending a few minutes talking shop. One of the great tragedies of being a mathematician is that your papers are read so seldom. On the average ten people will read the introduction to a paper and perhaps two of these will actually study the paper. It's difficult to know how to deal with this problem. One strategy which will at least get you one more reader, is to collaborate with someone. I think Israel early on caught on to this, and I imagine that by this time most of the analysts in the world have collaborated with him. He continues relentlessly in this pursuit; he visits his neighbour Harry Dym at the Weizmann Institute regularly, he spends several months a year in Amsterdam working with Rien Kaashoek, several weeks in Maryland with Seymour Goldberg, a couple of weeks here in Calgary with Peter Lancaster, and on the rare occasions when he is in Tel Aviv, he takes care of his many students.

In this book the authors try to bridge the gap between the treatments of matrix theory and linear algebra. It is aimed at graduate and advanced undergraduate students seeking a foundation in mathematics, computer science, or engineering. It will also be useful as a reference book for those working on matrices and linear algebra for use in their scientific work.

This book is dedicated to the memory of Israel Gohberg (1928-2009) - one of the great mathematicians of our time - who inspired innumerable fellow mathematicians and directed many students. The volume reflects the wide spectrum of Gohberg's mathematical interests. It consists of more than 25 invited and peer-reviewed original research papers written by his former students, co-authors and friends. Included are contributions to single and multivariable operator theory, commutative and non-commutative Banach algebra theory, the theory of matrix polynomials and analytic vector-valued functions, several variable complex function theory, and the theory of structured matrices and operators. Also treated are canonical differential systems, interpolation, completion and extension problems, numerical linear algebra and mathematical systems theory.

R. S. PHILLIPS I am very gratified to have been asked to give this introductory talk for our honoured guest, Israel Gohberg. I should like to begin by spending a few minutes talking shop. One of the great tragedies of being a mathematician is that your papers are read so seldom. On the average ten people will read the introduction to a paper and perhaps two of these will actually study the paper. It's difficult to know how to deal with this problem. One strategy which will at least get you one more reader, is to collaborate with someone. I think Israel early on caught on to this, and I imagine that by this time most of the analysts in the world have collaborated with him. He continues relentlessly in this pursuit; he visits his neighbour Harry Dym at the Weizmann Institute regularly, he spends several months a year in Amsterdam working with Rien Kaashoek, several weeks in Maryland with Seymour Goldberg, a couple of weeks here in Calgary with Peter Lancaster, and on the rare occasions when he is in Tel Aviv, he takes care of his many students.

In this article we shall use two special classes of reproducing kernel Hilbert spaces (which originate in the work of de Branges [dB) and de Branges-Rovnyak [dBRl), respectively) to solve matrix versions of a number of classical interpolation problems. Enroute we shall reinterpret de Branges' characterization of the first of these spaces, when it is finite dimensional, in terms of matrix equations of the Liapunov and Stein type and shall subsequently draw some general conclusions on rational m x m matrix valued functions which are "J unitary" a.e. on either the circle or the line. We shall also make some connections with the notation of displacement rank which has been introduced and extensively studied by Kailath and a number of his colleagues as well as the one used by Heinig and Rost [HR). The first of the two classes of spaces alluded to above is distinguished by a reproducing kernel of the special form K (>.) = J - U(>')JU(w)* (Ll) w Pw(>') , in which J is a constant m x m signature matrix and U is an m x m J inner matrix valued function over ~+, where ~+ is equal to either the open unit disc ID or the open upper half plane (1)+ and Pw(>') is defined in the table below.

Thefollowing topics ofmathematical analysishavebeen developed in the last?fty years: thetheoryoflinearcanonicaldi?erentialequationswithperiodicHamilto- ans, the theory of matrix polynomials with selfadjoint coe?cients, linear di?er- tial and di?erence equations of higher order with selfadjoint constant coe?cients, andalgebraicRiccati equations.All of these theories, and others, arebased on r- atively recent results of linear algebra in spaces with an inde?nite inner product, i.e., linear algebra in which the usual positive de?nite inner product is replaced by an inde?nite one. More concisely, we call this subject inde?nite linear algebra. This book has the structureof a graduatetext in which chaptersof advanced linear algebra form the core. The development of our topics follows the lines of a usual linear algebra course. However, chapters giving comprehensive treatments of di?erential and di?erence equations, matrix polynomials and Riccati equations are interwoven as the necessary techniques are developed. The main source of material is our earlier monograph in this ?eld: Matrices and Inde?nite Scalar Products, 40]. The present book di?ers in objectives and material.Somechaptershavebeenexcluded, othershavebeenadded, andexercises have been added to all chapters. An appendix is also included. This may serve as a summary and refresher on standard results as well as a source for some less familiar material from linear algebra with a de?nite inner product. The theory developed here has become an essential part of linear algebra. This, together with the many signi?cant areas of application, and the accessible style, make this book useful for engineers, scientists and mathematicians al

This scarce antiquarian book is a selection from Kessinger Publishing's Legacy Reprint Series. Due to its age, it may contain imperfections such as marks, notations, marginalia and flawed pages. Because we believe this work is culturally important, we have made it available as part of our commitment to protecting, preserving, and promoting the world's literature. Kessinger Publishing is the place to find hundreds of thousands of rare and hard-to-find books with something of interest for everyone

This text covers several aspects and solutions of the problems of linear vibrating systems with a finite number of degrees of freedom. It offers a detailed account of the part of the theory of matrices necessary for efficient problem-solving, beginning with the first four chapters' focus on developing the necesary tools in matrix theory. The following chapters present numerical procedures for the relevant matrix formulations and the relevant theory of differential equations. The book is directed toward a wide audience of applied mathematicans, scientists, and engineers who are interested in these problems from either practical or theoretical points of view. Although mathematically sound, the treatment involves readers in a minimum of mathematical abstraction. A familiarity and facility with matrix theory is assumed, along with a knowlege of elementary calculus, including the rudiments of the theory of functions of a complex variable. Unabridged republication of the edition published by Pergamon Press, Oxford, 1966. Preface. Bibliographical Notes. References. Index.