Relative perturbation results for matrix eigenvalues and singular values

Perturbation bounds for eigenvalues of diagonalizable matrices and singular values

Three Absolute Perturbation Bounds for Matrix Eigenvalues Imply Relative Bounds

We show that three well-known perturbation bounds for matrix eigenvalues imply relative bounds: the Bauer-Fike and Hooman-Wielandt theorems for diagonalisable matrices, and Weyl's theorem for Hermitian matrices. As a consequence, relative perturbation bounds are not necessarily stronger than absolute bounds; and the conditioning of an eigenvalue in the relative sense is the same as in the absol...

Matrix Reconstruction with Prescribed Diagonal Elements, Eigenvalues, and Singular Values

DIAGONAL ELEMENTS, EIGENVALUES, AND SINGULAR VALUES DRAFT AS OF April 30, 2013 SHENG-JHIH WU AND MOODY T. CHU Abstract. Diagonal entries and eigenvalues of a Hermitian matrix, diagonal entries and singular values of a general matrix, and eigenvalues and singular values of a general matrix satisfy necessarily some majorization relationships which turn out also to be sufficient conditions. The in...

Relative perturbation bounds for the eigenvalues of diagonalizable and singular matrices – Application of perturbation theory for simple invariant subspaces

Perturbation bounds for the relative error in the eigenvalues of diagonalizable and singular matrices are derived by using perturbation theory for simple invariant subspaces of a matrix and the group inverse of a matrix. These upper bounds are supplements to the related perturbation bounds for the eigenvalues of diagonalizable and nonsingular matrices. © 2006 Elsevier Inc. All rights reserved. ...

Eigenvalues, singular values, and Littlewood-Richardson Coefficients

Chi-Kwong Li Department of Mathematics, College of William and Mary, Williamsburg, Virginia 23187-8795, USA E-mail: [email protected] We briefly describe some recent results on inequalities relating the eigenvalues of the sum of Hermitian or real matrices, and how to use these them inequalities relating the eigenvalues and singular values of a matrix and its submatrices. These results are joint ...