Householder正交矩陣的新觀點

Abstract

文獻中有許多的方法可建立正交矩陣，Householder利用鏡射導得正交對稱矩陣。本文提出奇數階與偶數階Householder矩陣，均可分別由eAt與eiBt導得，其中A為反對稱實矩陣，B為對稱實矩陣，t為某特定時間。本文並分別舉一階到五階的例子，說明Householder矩陣均可由本文新觀點導得。It is well known that many approaches can obtain the orthogonal matrix. Householder employed the mirror mapping to derive the symmetric orthogonal matrix. The Householder matrices of odd and even orders are found to have the matrix forms of eAt and eiBt, respectively, where A is an anti-symmetric matrix, B is a symmetric matrix and t is a specified time. One by one to five by five Householder matrices are constructed by the proposed formulation.