高师理科学刊2026，Vol.46Issue(2)：9-13,5.DOI:10.3969/j.issn.1007-9831.2026.02.003
一道全国大学生数学竞赛决赛试题的推广
The generalization of a problem from the final of Chinese mathematics competition for college students
摘要
Abstract
Regarding a final competition question from the 2024 Chinese mathematics competition for college students,the original matrix equation AB=A+B is generalized to h(A)ABg(A)=kf(A)+lh(A)Bg(A)(kl ≠0),a systematic framework is established for solving such problems.Specific special cases of f(A),g(A),h(A)are applied to concrete examples,which provides both theoretical foundation and practical methodologies for addressing similar mathematical challenges.关键词
对角矩阵/特征值/特征向量Key words
diagonal matrix/eigenvalue/eigenvector分类
数理科学引用本文复制引用
薛维顺,薛宾..一道全国大学生数学竞赛决赛试题的推广[J].高师理科学刊,2026,46(2):9-13,5.基金项目
山西省高等学校省级教学改革创新项目(J20231854) （J20231854）
