The stable solutions of quadratic matrix equations
Authors:
Stephen Campbell and John Daughtry
Journal:
Proc. Amer. Math. Soc. 74 (1979), 1923
MSC:
Primary 15A24; Secondary 47A55
MathSciNet review:
521866
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Abstract: The authors determine which solutions K to the quadratic matrix equation are ``stable'' in the sense that all small changes in the coefficients of the equation produce equations some of whose solutions are close to K (in the metric determined by the operator norm). Our main result is that a solution is stable if and only if it is an isolated solution. (The isolated solutions already have a simple characterization in terms of the coefficient matrices.) It follows that each equation has only finitely many stable solutions. Equivalently, we identify the stable invariant subspaces for an operator T on a finitedimensional space as the isolated invariant subspaces.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002993919790521866X
PII:
S 00029939(1979)0521866X
Keywords:
Perturbation theory,
stable invariant subspaces,
quadratic matrix equations
Article copyright:
© Copyright 1979
American Mathematical Society
