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Lower bound estimation for the separation of two matrices

โœ Scribed by Shu-Fang Xu


Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
592 KB
Volume
262
Category
Article
ISSN
0024-3795

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โœฆ Synopsis


We give some lower bounds on the separations sep,( A, B), sepl A, B), and sep,( A, B). The bounds h s ow that the separation of two matrices A and B is closely related to the separation between the spectral sets of A and B, the structure of the Jordan canonical forms of A and B, and the departures from normality of A and B.


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We give a lower bound for the second smallest eigenvalue of Laplacian matrices in terms of the isoperimetric number of weighted graphs. This is used to obtain an upper bound for the real parts of the nonmaximal eigenvalues of irreducible nonnegative matrices.