guan yu jing xiang ju zhen yu pu ju zhen
Author(s): Tong Wen-ting
Pages: 109-118
Year: 1982 Issue: 1
Journal: Journal of Mathematical Research and Exposition
Keyword: 谱矩阵; 正定Hermite矩阵; 引理; 恒正性; Euclid范数; 定理1; 齐次性; 等价; 矩阵类; 正规矩阵;
Abstract: Let Ra and sp be the sets of nxn radial matrices and nxn spectral matrices, respectively. In this paper we give some characterizations of Ra and Sp. Specially, we give the following results:Theorem 1. For every , the following statemens are equivalent:23 , where m≥p, and p is degree of the minimal polynomial of A; 4 , where P(A) denotes the spectral radius of A; Theorem 2. For every , the following statements are equivalent:2 ;3 .In addition, we give the following results:Theorem 3. Let A, then1 ;2 ;3 .Theorem 4. Let , then1 ;2 .Theorem 5, Let then .Theorem 6. ,where No is the set of normal matrices.
Pages: 109-118
Year: 1982 Issue: 1
Journal: Journal of Mathematical Research and Exposition
Keyword: 谱矩阵; 正定Hermite矩阵; 引理; 恒正性; Euclid范数; 定理1; 齐次性; 等价; 矩阵类; 正规矩阵;
Abstract: Let Ra and sp be the sets of nxn radial matrices and nxn spectral matrices, respectively. In this paper we give some characterizations of Ra and Sp. Specially, we give the following results:Theorem 1. For every , the following statemens are equivalent:23 , where m≥p, and p is degree of the minimal polynomial of A; 4 , where P(A) denotes the spectral radius of A; Theorem 2. For every , the following statements are equivalent:2 ;3 .In addition, we give the following results:Theorem 3. Let A, then1 ;2 ;3 .Theorem 4. Let , then1 ;2 .Theorem 5, Let then .Theorem 6. ,where No is the set of normal matrices.
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