A quadratic form \(\text{tr}(AX^ 2)\) and its application
type: Item
instance of: scholarly article
title: A quadratic form \(\text{tr}(AX^ 2)\) and its application
zbMATH Open document ID: 0888.11014
DOI: 10.1016/S0024-3795(97)00002-5
author: Mitsuru Kuroda
published in: Linear Algebra and its Applications
publication date: 1997-11-23T00:00:00Z
review text: 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 \(M_2(F_q)\).
Mathematics Subject Classification ID: 11E04
Mathematics Subject Classification ID: 15B33
Mathematics Subject Classification ID: 11L05
zbMATH DE Number: 1083217
zbMATH Keywords: trace form
zbMATH Keywords: matrix algebra
zbMATH Keywords: Gauss sum
zbMATH Keywords: quadratic form
reviewed by: Krzysztof Kozioł
MaRDI profile type: Publication
cites work: Q3999066
cites work: Q4771383
cites work: Q5607309
cites work: Numbers of solutions of equations in finite fields
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description: scientific article; zbMATH DE number 1083217