皮皮 发表于 2007-8-21 23:19

[求助]矩阵分解 急！急！

<span style="FONT-SIZE: 10.5pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 12.0pt; mso-ascii-font-family: &quot;Times New Roman&quot;; mso-hansi-font-family: &quot;Times New Roman&quot;; mso-bidi-font-family: &quot;Times New Roman&quot;; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA;">矩阵论中，一个</span><span lang="EN-US" style="FONT-SIZE: 10.5pt; FONT-FAMILY: &quot;Times New Roman&quot;; mso-bidi-font-size: 12.0pt; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA; mso-fareast-font-family: 宋体;">n</span><span style="FONT-SIZE: 10.5pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 12.0pt; mso-ascii-font-family: &quot;Times New Roman&quot;; mso-hansi-font-family: &quot;Times New Roman&quot;; mso-bidi-font-family: &quot;Times New Roman&quot;; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA;">阶方阵可以唯一的分解为一个酉矩阵和一个正对角元的上三角矩阵的乘积。请问这个</span><span lang="EN-US" style="FONT-SIZE: 10.5pt; FONT-FAMILY: &quot;Times New Roman&quot;; mso-bidi-font-size: 12.0pt; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA; mso-fareast-font-family: 宋体;">n</span><span style="FONT-SIZE: 10.5pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 12.0pt; mso-ascii-font-family: &quot;Times New Roman&quot;; mso-hansi-font-family: &quot;Times New Roman&quot;; mso-bidi-font-family: &quot;Times New Roman&quot;; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA;">阶方阵是否可唯一分解为一个酉矩阵（或正交阵）和一个正对角元的下三角矩阵的乘积。若可以，如何分解？</span>

madio 发表于 2007-8-22 01:08

证明方法是一样的吧？就是构造一组标准正交基！

madio 发表于 2007-8-22 11:49

<p>利用矩阵的QR分解，只要取Q<sub>1</sub>=(Q<sup>-1</sup>)<sup>T</sup>,L=(R<sup>-1</sup>)<sup>T</sup>,这样就是QL分解了！</p>

皮皮 发表于 2007-8-22 13:17

非常感谢！！

away 发表于 2007-9-3 08:55

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