非负定阵元素的扰动和正定完备化

The Perturbation of Elements of Nonnegative Definite Matrices and Positive Definite Completion

在保持非负定性不变的前提下,本文对矩阵每一元素容许多大的扰动作了进一步的研究, 将本文的结论和C．R．Johnson提出的部分正定阵的正定完备化进行比较,容易发现对已知的正定矩阵求扰动,本文的结论比用C．R.Johnson的正定完备化计算扰动形式上更简单,同时也给出了不同于C．R．Johnson的部分正定阵的正定完备化表示的另外一个公式,推出了这些正定完备化矩阵应具有的若干性质．

This paper studies the range of its elements permitted to ensure nonnegative definite matrices keep nonnegative. Compared with the positive definite completions problem of partial hermitian matrices by C. R. Johnson, we find our result is simpler than C. R. Johnson＇s in the matter of studying the range of elements of completely known positive definite matrices. Moreover, we give another formula of positive definite completion problem different from C. R. Johnson＇s. and some properties of all these positive definite completion matrices.