Matrix analysis

Linear algebra and matrix theory have long been fundamental tools in mathematical disciplines as well as fertile fields for research. In this book the authors present classical and recent results of matrix analysis that have proved to be important to applied mathematics. Facts about matrices, beyond those found in an elementary linear algebra course, are needed to understand virtually any area of mathematical science, but the necessary material has appeared only sporadically in the literature and in university curricula. As interest in applied mathematics has grown, the need for a text and reference offering a broad selection of topics in matrix theory has become apparent, and this book meets that need. This volume reflects two concurrent views of matrix analysis. First, it encompasses topics in linear algebra that have arisen out of the needs of mathematical analysis. Second, it is an approach to real and complex linear algebraic problems that does not hesitate to use notions from analysis. Both views are reflected in its choice and treatment of topics. In This Book The Authors Present Classical And Recent Results For Matrix Analysis That Have Proved To Be Important To Applied Mathematics. Facts About Matrices, Beyond Those Found In An Elementary Linear Algebra Course, Are Needed To Understand Virtually Any Area Of Mathematics, And The Necessary Material Has Only Occurred Sporadically In The Literature And University Curricula. As The Interest In Applied Mathematics Has Grown, The Need For A Text And A Reference Work Offering A Broad Selection Of Topics Has Become Apparent, And This Book Aims To Meet That Need. This Book Will Be Welcomed As An Undergraduate Or Graduate Textbook For Students Studying Matrix Analysis. The Authors Assume A Background In Elementary Linear Algebra And Knowledge Of Rudimentary Analytical Concepts. They Begin With A Review And Discussion Of Eigenvalues And Eigenvectors. The Following Chapters Each Treat A Major Topic In Depth. This Volume Should Be Useful Not Only As A Text, But Also As A Self-contained Reference Work To A Variety Of Audiences In Other Scientific Fields. Review And Miscellanea -- Eigenvalues, Eigenvectors, And Similarity. Roger A. Horn, Charles R. Johnson. Includes Index. Bibliography: P. 543-546. The purpose of this chapter is to catalog briefly, without proof, a number of useful concepts and facts, many of which implicity or explicity underlie the material covered in the main portion of the book. Roger A. Horn, Charles R. Johnson. Includes Bibliographical References (p. 543-546) And Index.