矩阵值Caratheodory函数广义块Pick矩阵的秩不变性

Lasarow推导出矩阵值Caratheodory函数的第一、第二型广义块Pick矩阵及其变型的秩不变性.这些矩阵由同一个Caratheodory函数的值与它的直到某阶的导数值确定.利用文献中提出的块Toeplitz向量方法,该文断言,这些块矩阵的秩分别相关并重合于具有秩不变性的块Toeplitz矩阵的秩,从而改进了这两类广义块Pick矩阵的秩不变性结论的证明.

数量对合矩阵的线性组合的秩的不变性

若矩阵A、B满足A^2=λ~2I、B^2=μ~2I(λμ≠0),称A、B都是数量对合矩阵.当非零复数a、b、u、v满足aλ+bμ≠0、μλ+vμ≠0时,我们证明了数量对合矩阵A、B与单位矩阵Ⅰ的线性组合的秩总是相等,并且是一个与a、b、u,v选择都无关的常数.应用所得到数量对合矩阵的线性组合的秩的不变性,可推广已有文献的关于对合矩阵的相应结果.

幂等矩阵乘积方幂线性组合的秩等式

应用矩阵与幂等矩阵Jordan积的秩的性质,得到了一般矩阵与幂等矩阵乘积方幂线性组合秩的不变性,概括并改进了已有的相关结果.

Invariance of Numerical Character of Matrix Products and Their Statistical Applications

To study the invariance of numerical character of matrix products and their statistical applications by matrix theory and linear model theory. Necessary and sufficient conditions are established for the product AB -C to have its numerical characters invariant with respect to every minimum norm g inverse, respectively. The algebraic results derived are then applied to investigate relationships among BLUE, WLSE and OLSE under the general Gauss? Markoff model.