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.
β¦ LIBER β¦
Criteria for positive definiteness of some band matrices
β 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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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