Perturbation Bounds for Matrix Eigenvalues contains a unified exposition of spectral variation inequalities for matrices. The text provides a complete and self-contained collection of bounds for the distance between the eigenvalues of two matrices, which could be arbitrary or restricted to special classes. The book s emphasis on sharp estimates, general principles, elegant methods, and powerful techniques, makes it a good reference for researchers and students. For the SIAM Classics edition, the author has added over 60 pages of new material, which includes recent results and discusses the important advances made in the theory, results, and proof techniques of spectral variation problems in the two decades since the book s original publication. Audience This updated edition is appropriate for use as a research reference for physicists, engineers, computer scientists, and mathematicians interested in operator theory, linear algebra, and numerical analysis. The text is also suitable for a graduate course in linear algebra or functional analysis. Contents Preface to the Classics Edition; Preface; Introduction; Chapter 1: Preliminaries; Chapter 2: Singular values and norms; Chapter 3: Spectral variation of Hermitian matrices; Chapter 4: Spectral variation of normal matrices; Chapter 5: The general spectral variation problem; Chapter 6: Arbitrary perturbations of constrained matrices; Postscripts; References; Supplements 1986 2006; Chapter 7: Singular values and norms; Chapter 8: Spectral variation of Hermitian matrices; Chapter 9: Spectral variation of normal matrices; Chapter 10: Spectral variation of diagonalizable matrices; Chapter 11: The general spectral variation problem; Chapter 12: Arbitrary perturbations of constrained matrices; Chapter 13: Related Topics; Bibliography; Errata.