给出两个改进的算子闭值域定理，并对相关算子值域问题进行探讨。
Two improved theorems of closed operator range are given, and the issues related to operator range are discussed.
在传统规范形基础上，证明了只有线性算子值域补空间上的近恒同变换才能化简高阶规范形。
It is proved that only the transformations on linear operators' complementary subspace can be used to simplify high order normal form based on conventional normal form (CNF).
在本篇论文中，我们研究两类算子的数值域。
In this thesis, we study the numerical ranges of two kinds of operators.
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