论文标题
通勤魔术广场矩阵
Commuting Magic Square Matrices
论文作者
论文摘要
我们回顾了一种已知的方法，即将两个级别的M和N与All-Onnos矩阵复合，以形成两个order Mn的魔法正方形矩阵。我们表明这些复合的矩阵通勤。简单的公式是针对其Jordan形式和奇异价值分解的。我们验证是否可以通过复合来构建常规（联想）和pandiagonal通勤正方形。在特殊情况下，复合矩阵相似。考虑到将复合概括为更广泛的通勤魔法正方形。三个数字示例说明了我们的理论结果。
We review a known method of compounding two magic square matrices of order m and n with the all-ones matrix to form two magic square matrices of order mn. We show that these compounded matrices commute. Simple formulas are derived for their Jordan form and singular value decomposition. We verify that regular (associative) and pandiagonal commuting magic squares can be constructed by compounding. In a special case the compounded matrices are similar. Generalization of compounding to a wider class of commuting magic squares is considered. Three numerical examples illustrate our theoretical results.
