摘要
研究交换环上复合伴随矩阵的性质, 证明交换环上幂等 (幂零,幂单 )矩阵的复合伴随矩阵还是幂等(幂零,幂单)矩阵, 讨论交换环上复合伴随矩阵的Smith标准形,建立交换环上矩阵A的秩与A的复合伴随矩阵C*k (A)的秩之间的关系.
Some properties of compound adjoint matrices over commutative rings are considered. It is proved that the compound adjoint matrix of an idempotent (nilpotent, unipotent) matrix over commutative rings is idempotent (nilpotent, unipotent). Smith normal forms of compound adjoint matrices over any commutative ring are discussed. The relation between the rank of a matrix and the rank of its compound adjoint matrix over any commutative ring is given.
出处
《黑龙江大学自然科学学报》
CAS
北大核心
2005年第1期113-116,共4页
Journal of Natural Science of Heilongjiang University
关键词
复合伴随矩阵
幂等(幂零
幂单)矩阵
Smith标准形
compound adjoint matrix
idempotent matrix
nilpotent matrix
unipotent matrix
Smith normal form
