Linear Algebra lecture10 note
Four fundamental subspaces( for matrix A)
if A is m by n matrix:
Column space C(A) in Rm (列空间在m维实空间中)
Null space N(A) in Rn
Row space C(A^)(^代表转置)in Rn (all combinations of rows=all columns of A^)
Null space of A^ N(A^) in Rm (left null space of A 左零空间)
C(R) ≠ C(A)
different column space, same row space
“行变换不会对行空间产生影响,但“列空间”发生了变化
Basis for row space is first r rows of R
It’s called 基的最简形式
考虑:N(A^)
观察以上形式,所以称之为左零空间
由Gauss-Jordan 方法可得:
我们在矩阵右侧增广矩阵,并进行相同的变换
let’s check
求矩阵的左零空间,试着找一个产生零行向量的行组合
Linear Algebra lecture10 note的更多相关文章
- Linear Algebra lecture1 note
Professor: Gilbert Strang Text: Introduction to Linear Algebra http://web.mit.edu/18.06 Lecture 1 ...
- Linear Algebra lecture9 note
Linear independence Spanning a space Basis and dimension 以上概念都是针对a bunch of vectors, 不是矩阵里的概念 Supp ...
- Linear Algebra lecture8 note
Compute solution of AX=b (X=Xp+Xn) rank r r=m solutions exist r=n solutions unique example: 若想方程有解 ...
- Linear Algebra lecture7 note
Computing the nullspace (Ax=0) Pivot variables-free variables Special solutions: rref( A)=R rank o ...
- Linear Algebra lecture6 note
Vector spaces and subspaces Column space of A solving Ax=b Null space of A Vector space requiremen ...
- Linear Algebra Lecture5 note
Section 2.7 PA=LU and Section 3.1 Vector Spaces and Subspaces Transpose(转置) example: 特殊情况,对称 ...
- Linear Algebra lecture4 note
Inverse of AB,A^(A的转置) Product of elimination matrices A=LU (no row exchanges) Inverse of AB,A^(A ...
- Linear Algebra lecture3 note
Matrix multiplication(4 ways!) Inverse of A Gauss-Jordan / find inverse of A Matrix multiplication ...
- Codeforces Gym101502 B.Linear Algebra Test-STL(map)
B. Linear Algebra Test time limit per test 3.0 s memory limit per test 256 MB input standard input ...
随机推荐
- linux内核学习之四 系统调用
一 概念区分 提到linux系统调用,不得不区分几个比较容易混淆的概念: 系统调用:系统调用就是一种特殊的接口.通过这个接口,用户可以访问内核空间.系统调用规定了用户进程进入内核的具体位置. 应用程 ...
- Linq Group By
TableA { Id int, Name string, Group int Score int } 从 Id Name Group Score 1 张三 A 70 2 李四 A 80 3 王五 ...
- css3--布局正六边形
怎样布局正六边形?-->如果不能直接布局,就只能采用图形的组合.-->既然是正六边形,则: -->AB=2分之根号3乘2倍的边长,也就是对于矩形ABCD来说,AB是BD的根号3倍(也 ...
- fzu2028
//Accepted 7324 KB 203 ms /* source:fzu2028 time :2015.5.29 by :songt */ /*题解: 树链剖分 单点更新,求路径和 */ #in ...
- SQL-表的各种查查查
use Student gocreate table student1(code int,name varchar (20),sex char(10),tizhong decimal(18,1),ag ...
- Windows7+VS2010下OpenGL的环境配置
http://johnhany.net/2014/01/environment-for-opengl-with-vs2010/ OpenGL(Open Graphics Library)是一个开放的. ...
- mantis邮箱配置
1.修改/var/www/html/mantisbt-1.3.3/config下config_inc.php配置文件 以163邮箱为例 # --- Email Configuration --- $g ...
- Centos7搭建java+mysql环境
前几天买了个国外的vps,打算用来练练手,准备安装mysql+jdk+tomcat+git,然后就从网上找些资料开始安装. 1.准备工具 首先,需要连接到centos,这里我用的连接工具是xshell ...
- 【转】Native JavaScript Data-Binding
原文转自:http://www.sellarafaeli.com/blog/native_javascript_data_binding Two-way data-binding is such an ...
- Impossible to load an image in xcassets on bundle
Impossible to load an image in xcassets on bundle up vote5down votefavorite 3 I need to include imag ...