Singular value decomposition
2016-03-14 21:47
399 查看
SVD is a factorization of a real or complex matrix. It has many useful applications in signal processing and statistics.
Formally, the singular value decomposition of an real or complex matrix is a factorization of the form .
is an real or complex unitary matrix.
is an rectangular diagnal matrix with non-negative real numbers on the diagnal.
is an real or complex unitary matrix.
the diagnal entries of are known as the singular values of .
the left-singular vectors: columns of matrix .
the right-singular vectors: columns of matrix .
Wikipedia https://en.wikipedia.org/wiki/Singular_value_decomposition
unitary matrix : a complex square matrix is unitary if its conjugate transpose is also its inverse — that is, if
where is the identity matrix.
is the conjugate transpose of matrix .
identity matrix: is the square matrix with ones on the main diagnal and zeros else where.
the left-singular vectors of are a set of orthonormal eigenvectors of :
相关文章推荐
- 225. Implement Stack using Queues
- 232. Implement Queue using Stacks&225. Implement Stack using Queues
- 改良UIScrollView滚动视图
- UITableView介绍 之 AutoLayout下复杂cell的高度计算
- UI进阶——XML解析与Json解析
- 写的一个UGUI下Image控件做序列帧动画的小工具
- UEFI+GPT安装Windows7系统
- uva1583 Digit Generator && uva1584 Circular Sequence(水)
- 解决“Dynamic Web Module 3.0 requires Java 1.6 or newer.”错误
- UML建模----时序图(Sequence diagram)
- Error "The form cannot be rendered. This may be due to a misconfiguration......"的解决方案
- iOS设计之 多视图导航栏UINavigationController切换视图的简单设计
- POJ2524——Ubiquitous Religions 并查集基础
- 利用android提高的的insert,query,update,deleteAPI与execSql,rawQuery函数执行原生的插入,查询,更新,删除语
- UIViewController的基本概念与生命周期
- Android 图标上面添加提醒(二)使用开源UI类库 Viewbadger
- uva 11995——I Can Guess the Data Structure!
- poj 2533 Longest Ordered Subsequence 最长递增子序列
- AbstractQueuedSynchronizer分析
- iOS UIViewController的生命周期及iOS程序执行顺序