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On the principal minors of a matrix with a multiple eigenvalue

โœ Scribed by Kh. D. Ikramov

Book ID
106434263
Publisher
Springer US
Year
2006
Tongue
English
Weight
261 KB
Volume
137
Category
Article
ISSN
1573-8795

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An order O(2 n ) algorithm for computing all the principal minors of an arbitrary n ร— n complex matrix is motivated and presented, offering an improvement by a factor of n 3 over direct computation. The algorithm uses recursive Schur complementation and submatrix extraction, storing the answer in a

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For a matrix polynomial P (ฮป) and a given complex number ฮผ, we introduce a (spectral norm) distance from P (ฮป) to the matrix polynomials that have ฮผ as an eigenvalue of geometric multiplicity at least ฮบ, and a distance from P (ฮป) to the matrix polynomials that have ฮผ as a multiple eigenvalue. Then w