论文标题
在不确定内部产品空间中有通勤因子的极性分解上
On Polar Decompositions with Commuting Factors in Indefinite Inner Product Space
论文作者
论文摘要
该论文检查了极地分解对不确定的内部产物空间的概括。研究了必要的一般理论，并给出了一些一般结果。论文的主要部分侧重于具有通勤因素的极性分解：首先，给出了极地分解与通勤因子和正常矩阵之间联系的证明。然后，研究了此类分解的某些特性，并表明这些因素的交换性仅取决于自相关部分。最终，在没有改变空间结构的相似性转换下研究了具有通勤因子的极性分解。为此，正常形式被分解和分析。
This thesis examins a generalisation of polar decompositions to indefinite inner product spaces. The necessary general theory is studied and some general results are given. The main part of the thesis focuses on polar decompositions with commuting factors: First, a proof for a generalisation of the link between polar decomposition with commuting factors and normal matrices is given. Then, some properties of such decompositions are studied and it is shown that the commutativity of the factors only depends on the selfadjoint part. Eventually, polar decompositions with commuting factors are studied under similarity transformations that do not alter the structure of the space. For this purpose, normal forms are decomposed and analysed.
