This book is unique. It contains a detailed account of all important relations in the analytic theory of determinants from the classical work of Laplace, Cauchy and Jacobi in the 18th and 19th centuries, to the most recent 20th century developments. Several contributions have never been published before. Mathematicians, physicists and engineers who wish to becom acquainted with modern developments in the analytic theory of determinants will find this book indispensible.

Klappentext

A unique and detailed account of all important relations in the analytic theory of determinants, from the classical work of Laplace, Cauchy and Jacobi to the latest 20th century developments. The first five chapters are purely mathematical in nature and make extensive use of the column vector notation and scaled cofactors. They contain a number of important relations involving derivatives which prove beyond a doubt that the theory of determinants has emerged from the confines of classical algebra into the brighter world of analysis. Chapter 6 is devoted to the verifications of the known determinantal solutions of several nonlinear equations which arise in three branches of mathematical physics, namely lattice, soliton and relativity theory. The solutions are verified by applying theorems established in earlier chapters, and the book ends with an extensive bibliography and index. Several contributions have never been published before. Indispensable for mathematicians, physicists and engineers wishing to become acquainted with this topic.

Inhalt

Determinants, First Minors, and Cofactors.- A Summary of Basic Determinant Theory.- Intermediate Determinant Theory.- Particular Determinants.- Further Determinant Theory.- Applications of Determinants in Mathematical Physics.