摘要
证明了秩为k的正交投影矩阵,一定存在k阶主子阵,其Rayleigh商有一个正的下界.证明中综合使用了矩阵的奇异值、特征值、范数之间的优超关系以及酉矩阵和复合矩阵的性质,为进一步揭示正交投影矩阵的性质提供了一种可能.
In this paper we showed that for an orthogonal projection matrix with rank k, there exists an principal submatrix with order k of the matrix, such that its Rayleigh quotient has a positive lower bound. The proof was made by using the relation of the singular values, eigenvalues and norm of matrices, as well as the properties of unitary matrix and compound matrix.
出处
《华东师范大学学报（自然科学版）》
CAS
CSCD
北大核心
2012年第1期97-99,共3页
Journal of East China Normal University(Natural Science)
基金
上海财经大学"211工程"三期重点学科建设项目
上海财经大学研究生科研创新基金项目(XJJ-2011-395)
关键词
正交投影矩阵
奇异值
酉矩阵
复合矩阵
orthogonal projection matrix
singular value
unitary matrix
compound matrix
