矩阵的分块与应用

Study on the blocking and application for matrix

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.