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Criteria for positive definiteness of some band matrices

✍ Scribed by E. L. Allgower


Publisher
Springer-Verlag
Year
1970
Tongue
English
Weight
323 KB
Volume
16
Category
Article
ISSN
0029-599X

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✍ Junwei Shao; Xiaorong Hou πŸ“‚ Article πŸ“… 2010 πŸ› Elsevier Science 🌐 English βš– 152 KB

We present a new necessary and sufficient criterion to check the positive definiteness of Hermitian interval matrices. It is shown that an n Γ— n Hermitian interval matrix is positive definite if and only if its 4 n-1 (n -1)! specially chosen Hermitian vertex matrices are positive definite.

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Let \ be a nonnegative homogeneous function on R n . General structure of the set of numerical pairs ($, \*), for which the function (1&\ \* (x)) $ + is positive definite on R n is investigated; a criterion for positive definiteness of this function is given in terms of completely monotonic function