纺织高校基础科学学报
紡織高校基礎科學學報
방직고교기출과학학보
BASIC SCIENCES JOURNAL OF TEXTILE UNIVERSITIES
2013年
3期
313-317
,共5页
三次幂等矩阵%酉矩阵%压缩矩阵%极分解
三次冪等矩陣%酉矩陣%壓縮矩陣%極分解
삼차멱등구진%유구진%압축구진%겁분해
tripotent matrix%unitary matrix%contraction matrix%polar decomposition
利用代数的方法，对给定的两个非零三次幂等矩阵 P1，P2和酉矩阵U1，U2，讨论了线性组合 P＝ c1 P1＋ c2 P2保持三次幂等性系数所满足的充要条件。给出了使线性组合U ＝ c1U1＋ c2U2保持酉性时系数所满足的充分条件，其中c1，c2为非零的复数。利用矩阵极分解给出酉矩阵线性组合的性质刻画。
利用代數的方法，對給定的兩箇非零三次冪等矩陣 P1，P2和酉矩陣U1，U2，討論瞭線性組閤 P＝ c1 P1＋ c2 P2保持三次冪等性繫數所滿足的充要條件。給齣瞭使線性組閤U ＝ c1U1＋ c2U2保持酉性時繫數所滿足的充分條件，其中c1，c2為非零的複數。利用矩陣極分解給齣酉矩陣線性組閤的性質刻畫。
이용대수적방법，대급정적량개비령삼차멱등구진 P1，P2화유구진U1，U2，토론료선성조합 P＝ c1 P1＋ c2 P2보지삼차멱등성계수소만족적충요조건。급출료사선성조합U ＝ c1U1＋ c2U2보지유성시계수소만족적충분조건，기중c1，c2위비령적복수。이용구진겁분해급출유구진선성조합적성질각화。
Given two nonzero tripotent matrices P1 ,P2 and unitary matrices U1 ,U2 ,tripotency and unility problems of linear combinations that were preserved were discused by using algebra method .Some suffi-cient and necessary conditions of c1 P1 + c2 P2 were obtained .And some sufficient condition of c1U2 + c2U2 for a unitary matrix were given .The property of linear combinations of unitary matrices was character-ized .
