A quadratic form \(\text{tr}(AX^ 2)\) and its application
Trace forms \(\text{tr}(AX^2)\) on the matrix algebra \(M_n(F_q)\) over a finite field \(F_q\) (\(q\) odd) are classified for \(n = 2,3\). This classification and the Gauss sums are used to compute the number of solutions of the equation \(X_1^2 + \ldots + X_m^2 = B\) in \(M_2(F_q)\).
scientific article; zbMATH DE number 1083217