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Some determinant expansions and the matrix-tree theorem

โœ Scribed by J.W. Moon

Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
513 KB
Volume
124
Category
Article
ISSN
0012-365X

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โœฆ Synopsis

We derive an expansion for a certain determinant that involves two sets of formal variables. The result provides a unified approach to several known expansions including a generalized form of the matrix-tree theorem.

๐Ÿ“œ SIMILAR VOLUMES

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## Abstract The Szegล‘โ€“Widom Limit Theorem says that for certain __N__ ร— __N__ matrix functions __ฯ†__ defined on the unit circle, the asymptotic behavior of the determinants of the block Toeplitz matrices __T__~__n__~ (__ฯ†__) is given by equation image where __G__ [__ฯ†__ ] is the geometric mean of