论文标题
MATLABS魔术广场
Spectrum of MATLABs magic squares
论文作者
论文摘要
本文着眼于MATLAB的魔术（$ n $）功能产生的魔法正方形的特征值。魔术（$ n $）函数甚至构造了双重构造（$ n = 4k $）魔法正方形，甚至（$ n = 4k+2 $）魔术正方形和奇数（$ n = 2k+1 $）使用不同算法（$ n = 2k+1 $）。甚至魔术正方形是通过一种纵横交错的方法构建的，涉及反映中心方面的简单广场的条目。奇怪的魔法正方形是使用暹罗方法构建的。甚至使用低阶奇数魔法正方形（Strachey方法）构建单一的魔法正方形。我们获得了奇数和魔术平方的特征值的近似值，并在近似上证明了误差界限。为了完整，我们还获得了Matlab产生的双重魔法正方形的特征。光谱的近似涉及与G循环矩阵光谱以及使用Bauer-Fike定理的一些有趣的连接。
This article looks at the eigenvalues of magic squares generated by the MATLAB's magic($n$) function. The magic($n$) function constructs doubly even ($n = 4k$) magic squares, singly even ($n = 4k+2$) magic squares and odd ($n = 2k+1$) magic squares using different algorithms. The doubly even magic squares are constructed by a criss-cross method that involves reflecting the entries of a simple square about the center. The odd magic squares are constructed using the Siamese method. The singly even magic squares are constructed using a lower-order odd magic square (Strachey method). We obtain approximations of eigenvalues of odd and singly even magic squares and prove error bounds on the approximation. For the sake of completeness, we also obtain the eigenpairs of doubly even magic squares generated by MATLAB. The approximation of the spectra involves some interesting connections with the spectrum of g-circulant matrices and the use of Bauer-Fike theorem.
