论文标题
三个对角线的故事
A tale of three diagonalizations
论文作者
论文摘要
除了通过单一相似性转换对正常矩阵的对角化外，有时在量子理论应用中有时会出现另外两种类型的对角线化程序 - 奇异值分解和自动takagi分解。在这些教学笔记中，我们对最通用的$ 2 \ times 2 $矩阵进行了这些对角线化程序，为相应的对角线化是可能的，并在这三种情况下每种情况下都提供了明确的分析结果。
In addition to the diagonalization of a normal matrix by a unitary similarity transformation, there are two other types of diagonalization procedures that sometimes arise in quantum theory applications -- the singular value decomposition and the Autonne-Takagi factorization. In these pedagogical notes, we carry out each of these diagonalization procedures for the most general $2\times 2$ matrices for which the corresponding diagonalization is possible and provide explicit analytical results in each of the three cases.
