Relative eigenvalues of a definite matrix pair
نویسندگان
چکیده
منابع مشابه
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...
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For a symmetric positive semi-definite diagonally dominant matrix, if its off-diagonal entries and its diagonally dominant parts for all rows (which are defined for a row as the diagonal entry subtracted by the sum of absolute values of off-diagonal entries in that row) are known to a certain relative accuracy, we show that its eigenvalues are known to the same relative accuracy. Specifically, ...
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The spectral properties of Hermitian matrix polynomials with real eigenvalues have been extensively studied, through classes such as the definite or definitizable pencils, definite, hyperbolic, or quasihyperbolic matrix polynomials, and overdamped or gyroscopically stabilized quadratics. We give a unified treatment of these and related classes that uses the eigenvalue type (or sign characterist...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1990
ISSN: 0024-3795
DOI: 10.1016/0024-3795(90)90402-x