This is the only book devoted exclusively to Hessenberg and tridiagonal matrices. Hessenberg matrices are involved in Krylov methods for solving linear systems or computing eigenvalues and eigenvectors, in the QR algorithm for computing eigenvalues, and in many other areas of scientific computing (for instance, control theory). Matrices that are both upper and lower Hessenberg are tridiagonal. Their entries are zero except for the main diagonal and the subdiagonal and updiagonal next to it. Hessenberg and Tridiagonal Matrices: Theory and Examples presents known and new results; describes the theoretical properties of the matrices, their determinants, LU factorizations, inverses, and eigenvalues; illustrates the theoretical properties with applications and examples as well as numerical experiments; and considers unitary Hessenberg matrices, inverse eigenvalue problems, and Toeplitz tridiagonal matrices.

About the Author

G�rard Meurant is retired from the French Atomic Energy Commission (CEA), where he worked in applied mathematics from 1970 to 2008. He was research director at the time of his retirement. He is the author of more than 60 papers on numerical linear algebra and seven books.

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