The number of equivalence classes of nondegenerate bilinear and sesquilinear forms over a finite field

DOI10.1016/0024-3795(81)90097-5zbMath0472.15012OpenAlexW2021917420MaRDI QIDQ1158233

S. H. Smith

Publication date: 1981

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0024-3795(81)90097-5

zbMATH Keywords

finite fieldbilinear formsequivalence classessesquilinear forms

Mathematics Subject Classification ID

Quadratic forms over general fields (11E04) Matrices over special rings (quaternions, finite fields, etc.) (15B33) Quadratic and bilinear forms, inner products (15A63) Canonical forms, reductions, classification (15A21) General binary quadratic forms (11E16)

Related Items

Conjugacy class properties of the extension of \(\text{GL}(n,q)\) generated by the inverse transpose involution. ⋮ Real and strongly real classes in SL n (q) ⋮ Equivalence and normal forms of bilinear forms ⋮ ON THE NUMBER OF REAL CLASSES IN THE FINITE PROJECTIVE LINEAR AND UNITARY GROUPS ⋮ The number of pairs of quadratic forms over \(\mathbb{F}_q\) (\(q\) odd)

Cites Work

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• Pairs of commuting matrices over a finite field
• Congruence and conjunctivity of matrices
• On the conjugacy classes in the unitary, symplectic and orthogonal groups