(半)正/负定矩阵数学符号表示的科学性分析

Scientific Analysis of Mathematical Notation for Positive/Negative Definite or Semi-Definite Matrices

科学的数学符号表示方法对于科学研究工作具有很重要的意义。目前部分教材和文献中(半)正定和(半)负定矩阵的数学符号表示不够科学,易引起读者的误解,并由此导致错误的推论。因此,对这种表示方法的不科学性的指出与更正是非常必要的。本文对这种不科学的表示方法进行了深入的分析,并提出了两种较为科学的(半)正/负定矩阵的符号表示法,以弥补原来的符号表示法所存在的缺陷。这将有助于读者和编者正确地理解及恰当地应用(半)正和(半)负定矩阵于各类教学、科研与工程实践之中。

It is very important to use mathematic notations precisely in scientific research and investigation. At Present, the mathematical notation for positive/negative definite or semi--definite matrices is less correct in some textbooks and literatures. Such a matbematical notation may lead readers to misunderstanding and wrong derivation. It thus becomes very necessary to point out and correct this less-scientific notation. In this paper, we analyze the mathematic notation, and suggest two more--scientific notation for handling positive/negative definite or semi--definite matrices, The new notation could avoid the defects of the original mathematical notation, and, at the same time, could help readers understand and apply such a notation better.