Spaces of Hankel matrices over finite fields
β Scribed by Roy Meshulam
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 238 KB
- Volume
- 218
- Category
- Article
- ISSN
- 0024-3795
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π SIMILAR VOLUMES
It has been known for some time that every polynomial with coefficients from a finite field is the minimum polynomial of a symmetric matrix with entries from the same field. What have remained unknown, however, are the possible sizes for the symmetric matrices with a specified minimum polynomial and
Let F q be the finite field with q elements, q ΒΌ p n ; p 2 N a prime, and Mat 2:2 Γ°F q Γ the vector space of 2 Γ 2-matrices over F. The group GLΓ°2; FΓ acts on Mat 2;2 Γ°F q Γ by conjugation. In this note, we determine the invariants of this action. In contrast to the case of an infinite field, where
Connections between q-rook polynomials and matrices over finite fields are exploited to derive a new statistic for Garsia and Remmel's q-hit polynomial. Both this new statistic mat and another statistic for the q-hit polynomial recently introduced by Dworkin are shown to induce different multiset Ma
to helmut wielandt for his 90th birthday with much respect and many congratulations , where m X t is its minimal polynomial and c X t is its characteristic polynomial det tI -X . This condition is equivalent to requiring the vector space F d of 1 Γ d row vectors over F to be cyclic as an F X -modul