幺正矩阵的分解

参考文献：Dita P. Factorization of Unitary Matrices[J]. Journal of Physics A, 2003, 36(11): 2781-2789.

（我主机中的文件：《2003Dita.docx》《2003Dita.pdf》）

n*n 幺正矩阵 U(n) 的独立参数为 n² 个，证明如下：

结论：

　　Any unitary matrix  An can be factored into an ordered product of (2n-1) matrices of the form

${A_n} = \left[ {{d_n}{O_n}} \right]\left[ {d_{n - 1}^1O_{n - 1}^1} \right] \cdots \left[ {d_2^{n - 2}O_2^{n - 2}} \right]d_1^{n - 1}$

 1. 其中的 d 为 diagnol phase matrices, 一共 n 个。

$

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\[{d_n}{\rm{ = }}\left( {\begin{array}{*{20}{c}}

{{{\rm{e}}^{i{\varphi _1}}}}&{}&{}&{}\\

{}& \ddots &{}&{}\\

{}&{}& \ddots &{}\\

{}&{}&{}&{{{\rm{e}}^{i{\varphi _n}}}}

\end{array}} \right)\]% MathType!End!2!1!

 $

幺正矩阵的分解

原文：http://www.cnblogs.com/zhangshihao/p/7943940.html