Annali di Matematica Pura ed Applicata

, Volume 44, Issue 1, pp 245–250 | Cite as

Some matrix equations over a finite field

  • John H. Hodges


Explicit formulas are found for the number of solutions over a finite field of several matrix equations, for example:X′A+A′X=B. Conditons for solvability are also given.


Matrix Equation Symmetric Matrix Finite Field Hermitian Matrix Hermitian Form 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. [1]
    Garret Birkhoff andSaunders Maclane,A Survey of Modern Algebra, New York, 1941.Google Scholar
  2. [2]
    L. Carlitz,Representations by quadratic forms in a finite field, « Duke Mathematical Journal », vol. 21 (1954), pp. 123–137.zbMATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    L. Carlitz,Representations by skew forms in a finite field, « Archiv der Mathematik » vol. V (1954) pp. 19–31.CrossRefGoogle Scholar
  4. [4]
    L. Carlitz andJ. H. Hodges,Representations by Hermitian forms in a finite field, « Duke Mathematical Journal », vol. 22 (1955), pp. 393–405.zbMATHCrossRefMathSciNetGoogle Scholar
  5. [5]
    J. H. Hodges,The matric equation AX = B in a finite field, « American Mathematical Monthly », vol. 63 (1956), pp. 243–244.zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Swets & Zeitlinger B. V. 1978

Authors and Affiliations

  • John H. Hodges
    • 1
  1. 1.BuffaloU. S. A.

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