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Sylvester's law of inertia states that the number of positive, negative and zero eigenvalues of Hermitian matrices is preserved under congruence transformations.
Störungstheorie der Spektralzerlegung I
F. Rellich · 1937
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Perturbation Theory for Linear Operators
T. Kato · 1966
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Perturbation Theory of Eigenvalue Problems
F. Rellich · 1969
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Applied Numerical Linear Algebra
J. Demmel · 1997
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A generalization of the inertia theorem for quadratic matrix polynomials
B. Bilir and C. Chicone · 1998
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Constraint preconditioning for indefinite linear systems
C. Keller, N. I. M. Gould, and A. J. Wathen · 2000
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On the inertia law for normal matrices
K. D. Ikramov · 2001
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Canonical forms for Hermitian matrix pairs under strict equivalence and congruence
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Computing the common zeros of two bivariate functions via Bézout resultants
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Tropical roots as approximations to eigenvalues of matrix polynomials
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Efficient estimation of eigenvalue counts in an interval
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On Sylvester’s law of inertia for nonlinear eigenvalue problems
A. Kostić and H. Voss · 2013
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Spectral equivalence of matrix polynomials and the index sum theorem
F. De Terán, F. M. Dopico, and D. S. Mackey · 2014
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A demonstration of the theorem that every homogeneous quadratic polynomial is reducible by real orthogonal substitutions to the form of a sum of positive and negative squares
J. J. Sylvester
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On the sign characteristics of Hermitian matrix polynomials
V. Mehrmann, V. Noferini, F. Tisseur, and H. Xu · 2016
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