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On the eigenvalues of matrices

✍ Scribed by P. Turàn

Book ID
112746662
Publisher
Springer
Year
1961
Tongue
English
Weight
211 KB
Volume
54
Category
Article
ISSN
0373-3114

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We consider matrices containing two diagonal bands of positive entries. We show that all eigenvalues of such matrices are of the form rζ , where r is a nonnegative real number and ζ is a pth root of unity, where p is the period of the matrix, which is computed from the distance between the bands. We

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We consider the roots of two families of polynomials which can be derived as the characteristic polynomials of some (generalized) transfer matrices. We study the possible multiplicities and the number of real roots. Moreover, the number of roots lying inside the unit disk is determined, and bounds f