线性算子P—条件数的一些性质

众所周知,常用的线性算子的条件数有 k—条件数和 P—条件数。笔者讨论了 P—条件数的一些性质,得到如下主要结果:(1)给出了 P(T)=k(r)的充分必要条件;(2)给出了 P(T)=1时,线性算子 T 的谱的构成和 P(T)=1的一些条件;(3)把线性算子 P—条件数的一些性质推广到了伪 P—条件数的情形。

Some Porperties of P-Condition Number for Linear Operators

As known by all,the condition number of a linear operator T often used is K-condition number or P-condition number. This paper discusses the properties of P(T),obtaining the following results:(1)gives a sufficient and necessary condition for P(T)=k(T);(2)Presents the spectral structure of a linear operator T when P(T)=1 and gives some conditions for P(T) =1;(3)extends some properties of P(T)to the condition of pseudo-P-condition number.