The Factorization of a Matrix as the Commutator of Two Matrices
نویسنده
چکیده
Let P = f" + (I ,,) , the direct sum of the p x p identity matrix and the negative of the q x q ident ity matrix. The fo llowing theorem 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 which sati sfy X = AB BA are given. Methods are a lso given fo r de terminin g pairs of anti co mmuting P -orth"gona l, P -skew-symmetric matrices.
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