1. Eigenvalues, eigenvectors, and similarity; 2. Unitary similarity and unitary equivalence; 3. Canonical forms for similarity, and triangular factorizations; 4. Hermitian matrices, symmetric matrices, and congruences; 5. Norms for vectors and matrices; 6. Location and perturbation of eigenvalues; 7. Positive definite and semi-definite matrices; 8. Positive and nonnegative matrices; Appendix A. Complex numbers; Appendix B. Convex sets and functions; Appendix C. The fundamental theorem of algebra; Appendix D. Continuous dependence of the zeroes of a polynomial on its coefficients; Appendix E. Continuity, compactness, and Weierstrass' theorem; Appendix F. Canonical pairs.
The thoroughly revised and updated second edition of this acclaimed text has several new and expanded sections and more than 1,100 exercises.
Roger A. Horn is a Research Professor in the Department of Mathematics at the University of Utah. He is co-author of Topics in Matrix Analysis (Cambridge University Press, 1994). Charles R. Johnson is a Professor in the Department of Mathematics at the College of William and Mary. He is co-author of Topics in Matrix Analysis (Cambridge University Press, 1994).
Review of the first edition: 'The presentation is straightforward
and extremely readable. The authors' enthusiasm pervades the book,
and the printing is what we expect from this publisher. This will
doubtless be the standard text for years to come.' American
Scientist
Review of the first edition: 'The reviewer strongly recommends that
those working in either pure or applied linear algebra have this
book on their desks.' SIAM Review
Review of the first edition: 'There seems little doubt that the
book will become a standard reference for research workers in
numerical mathematics.' Computing Reviews
Review of the first edition: 'The authors have done an excellent
job of supplying linear algebraists and applied mathematicians with
a well-organized comprehensive survey, which can serve both as a
text and as a reference.' Linear Algebra and its Applications
'The book is well organized, completely readable, and very
enlightening. For researchers in matrix analysis, matrix
computations, applied linear algebra, or computational science,
this second edition is a valuable book.' Jesse L. Barlow, Computing
Reviews
'With the additional material and exceedingly clear exposition,
this book will remain the go-to book for graduate students and
researchers alike in the area of linear algebra and matrix theory.
I suspect there are few readers who will go through this book and
not learn many new things. It is an invaluable reference for anyone
working in this area.' Anne Greenbaum, SIAM Review
'The new edition is clearly a must-have for anyone seriously
interested in matrix analysis.' Nick Higham, Applied Mathematics,
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