咱们网站的这个公式编辑器,估计是后台生成图片后贴回来的,固定分辨率而且分辨率不高。
还不如先离线 latex 生成 pdf 后再截图上来
1. Why QR
When A and b are known, to solver the minimization of , where
.
The reduction of A to various canonical form via orthogonal transformations should use Householder reflections and Givens rotations.
2. preview on orthogonal matrix
2.1 Orthogonal matrix
2.2 rotation matrix is orthogonal matrix
is orthogonal and
is a rotation matrix.
If , then
is obtained by rotating
counterclockwise through an angle
.
2.3 reflection matrix is orthogonal matrix
is orthogonal and
is a reflection matrix.
If , then
is obtained by reflecting the vector
across the line defined by
That means and
are axial symmetry, looks like :
3. Householder transformation
未完待续 ... ...