附註:Includes bibliographical references (pages 432-453) and index.
Cover -- Table of Contents -- 1 Matrix Analysis -- 1.1 Introduction -- 1.2 Basic definitions and notation -- 1.3 Matrix inversion and determinants -- 1.4 Eigenvalues and eigenvectors -- 2 Vibrations of Discrete Systems -- 2.1 Introduction -- 2.2 Vibration of some simple systems -- 2.3 Transverse vibration of a beam -- 2.4 Generalised coordinates and Lagrange's equations: the rod -- 2.5 Vibration of a membrane and an acoustic cavity -- 2.6 Natural frequencies and normalmodes -- 2.7 Principal coordinates and receptances -- 2.8 Rayleigh's Principle -- 2.9 Vibration under constraint -- 2.10 Iterative and independent definitions of eigenvalues -- 3 Jacobi Matrices -- 3.1 Sturm sequences -- 3.2 Orthogonal polynomials -- 3.3 Eigenvectors of Jacobimatrices -- 3.4 Generalised eigenvalue problems -- 4 Inverse Problems for Jacobi Systems -- 4.1 Introduction -- 4.2 An inverse problemfor a Jacobimatrix -- 4.3 Variants of the inverse problem for a Jacobi matrix -- 4.4 Reconstructing a spring-mass system; by end constraint -- 4.5 Reconstruction by using modification -- 4.6 Persymmetric systems -- 4.7 Inverse generalised eigenvalue problems -- 4.8 Interior point reconstruction -- 5 Inverse Problems for Some More General Systems -- 5.1 Introduction: graph theory -- 5.2 Matrix transformations -- 5.3 The star and the path -- 5.4 Periodic Jacobimatrices -- 5.5 The block Lanczos algorithm -- 5.6 Inverse problems for pentadiagonal matrices -- 5.7 Inverse eigenvalue problems for a tree -- 6 Positivity -- 6.1 Introduction -- 6.2 Minors -- 6.3 A general representation of a symmetric matrix -- 6.4 Quadratic forms -- 6.5 Perron's theorem -- 6.6 Totally non-negativematrices -- 6.7 Oscillatory matrices -- 6.8 Totally positivematrices -- 6.9 Oscillatory systems of vectors -- 6.10 Eigenproperties of TNmatrices -- 6.11 u-line analysis -- 7 Isospectral Systems -- 7.1 Introduction -- 7.2 Isospectral flow -- 7.3 Isospectral Jacobi systems -- 7.4 Isospectral oscillatory systems -- 7.5 Isospectral b
摘要:"In this new edition the scope of the book has been widened to include topics such as isospectral systems - families of systems which all exhibit some specified behaviour; applications of the concept of Toda flow; new, non-classical approaches to inverse Sturm-Liouville problems; qualitative properties of the modes of some finite element models; and damage identification." "With its emphasis on analysis and qualitative results, rather than on computation, the book will appeal to researchers in vibration theory, matrix analysis, differential and integral equations, matrix analysis, non-destructive testing, modal analysis, vibration isolation, etc."--Jacket.
