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引用次数: 0
摘要
设P = f ' ' + (- I，，) P × P单位矩阵与负的q × q矩阵的正和。证明了下面的定理。EOHEM:如果X = cZ，其中Z是一个4 X 4的p -正交，p -斜对称矩阵，Ie I .;;;2，存在矩阵A和。d B，它们都是p正交和p偏对称的，所以X = AB - BA。给出了满足X = AB - BA的若干矩阵的求取方法。本文还给出了一种方法，用于确定变换P - 0 - 1、P - 1、P - 2等已知对称矩阵的非对称对。
The Factorization of a Matrix as the Commutator of Two Matrices
Let P = f " + (- I ,,) , the direct sum of the p x p identity matrix and the negative of the q x q ide n t ity matrix. The following th eo re m is proved. TH EOHEM: If X = cZ where Z is a 4 x 4 P-orthogonal , P-skew-symmetric matrix and Ie I .;;; 2, there exist matrices A an.d B, both of which are P-orthogollal and P-skew-symmetric, sach that X = AB - BA. Methods for o btaining certain matrices whi c h sati s fy X = AB - BA are given. Methods are a lso give n fo r de terminin g pairs of a nti co mmuting P -o rth"gona l, P -s kew-symmetri c matrices.
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