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矩阵的分块与应用 被引量:2

Study on the blocking and application for matrix
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摘要 针对矩阵的分块技巧在实际计算中的应用,运用矩阵的和与积的计算结果,分析讨论了若干半正定矩阵的线性组合的行列式的性质,还证明了L是李双函数类,对任意的f∈L,{ABB*L}≥0 f(B)2≤->f(A)f(C)类L中的元素是行列式、迹、酉不变范数.以此定理为工具,给出了一些矩阵的分块方法在矩阵不等式及线性映射中的应用。 This paper makes use of the conclusion of I product A≥0,B≥0A+B≥0 and II product A≥0,B≥0AB≥0.Where the matrix A is positive semi-definite when A≥0,AB=(aijbij) is the Hadamard product of matrix A and B.These two conclusions show that: Let L be dual function class,for arbitrary f∈L,(ABB*C)≥0|f(B)|2≤f(A)f(C),the element in class L is determinant,trace,unitarily invariant norm and so on.We use this theorem as a tool,and illustrate the use of block matrix method in matrix inequalities and linear map by giving instances.
作者 高振兴
出处 《辽宁师范大学学报(自然科学版)》 CAS 2011年第2期157-160,共4页 Journal of Liaoning Normal University:Natural Science Edition
关键词 分块矩阵 正半定矩阵 范数 矩阵不等式 block matrix positive semi-definite matrix normal number matrix inequality
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