householder进行矩阵QR分解

文章目录

• [1. Householder 进行QR分解](#1. Householder 进行QR分解)

1. Householder 进行QR分解

A = Q R (1) A=QR\tag1 A=QR(1)
A = 1 2 0 1 1 0 3 1 1 0 3 2 1 2 0 2 (2) A=\begin{bmatrix}1&2&0&1\\\\1&0&3&1\\\\1&0&3&2\\\\1&2&0&2\end{bmatrix}\tag2 A= 1111200203301122 (2)

从矩阵A中取出第一列 a 1 ⃗ = 1 , 1 , 1 , 1 T \vec{a_1}=1,1,1,1^T a1 =1,1,1,1T ， ∥ α 1 ∥ 2 \lVert \alpha_1\rVert_2 ∥α1∥2