We are concerned with the behavior of the minimum (maximum) eigenvalue A~0 "~ (A~ "~) of an (n + 1) X (n + 1) Hermitian Toeplitz matrix T~(f) where f is an integrable real-valued function. Kac, Murdoch, and Szeg5, Widom, Patter, and R. H. Chan obtained that A}~ 0 -rain f = O(1/n 2k) in the case whe
A survey of the eigenstructure properties of finite Hermitian Toeplitz matrices
✍ Scribed by Yves Genin
- Publisher
- SP Birkhäuser Verlag Basel
- Year
- 1987
- Tongue
- English
- Weight
- 831 KB
- Volume
- 10
- Category
- Article
- ISSN
- 0378-620X
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📜 SIMILAR VOLUMES
Let T be a skew-symmetric Toeplitz matrix with entries in a ®nite ®eld. For all positive integers n let n be the upper n  n corner of T, with nullity m n m n . The sequence fm n X n P Ng satis®es a unimodality property and is eventually periodic if the entries of T satisfy a periodicity condition.
Some geometry of Hermitian matrices of order three over GF(q 2 ) is studied. The variety coming from rank 2 matrices is a cubic hypersurface M 3 7 of PG(8, q) whose singular points form a variety H corresponding to all rank 1 Hermitian matrices. Beside M 3 7 turns out to be the secant variety of H.