Determinantal polynomials and the base polynomial of a square matrix over a finite field

Purpose – The author studies forms over finite fields obtained as the determinant of Hermitian matrices and use these determinatal forms to define and study the base polynomial of a square matrix over a finite field. Design/methodology/approach – The authors give full proofs for the new results, quoting previous works by other authors in the proofs. In the introduction, the authors quoted related references. Findings – The authors get a few theorems, mainly describing some monic polynomial arising as a base polynomial of a square matrix. Originality/value – As far as the author knows, all the results are new, and the approach is also new.