衡水学院学报
衡水學院學報
형수학원학보
JOURNAL OF HENGSHUI UNIVERSITY
2012年
1期
16-17
,共2页
矩阵相似%矩阵合同%实对称矩阵
矩陣相似%矩陣閤同%實對稱矩陣
구진상사%구진합동%실대칭구진
similarity of matrix%contract of matrix%real symmetric matrix
矩阵的相似与合同是截然不同的两个概念,本文给出了一般矩阵相似不合同、合同不相似的实例,给出了实对称矩阵合同与相似的充要条件,并得到实对称矩阵在正交变换条件下相似与合同达到了统一.
矩陣的相似與閤同是截然不同的兩箇概唸,本文給齣瞭一般矩陣相似不閤同、閤同不相似的實例,給齣瞭實對稱矩陣閤同與相似的充要條件,併得到實對稱矩陣在正交變換條件下相似與閤同達到瞭統一.
구진적상사여합동시절연불동적량개개념,본문급출료일반구진상사불합동、합동불상사적실례,급출료실대칭구진합동여상사적충요조건,병득도실대칭구진재정교변환조건하상사여합동체도료통일.
The similarity and contract of matrix are two distinct concepts.In this paper,we first discuss the examples of general matrices which have similarity but no contract or have contract but no similarity and then give the necessary and sufficient condition of similarity and contract for the real symmetric matrix.Finally we get the conclusion that the similarity agrees with the contract for the real symmetric matrix under orthogonal transform condition.
