[Bhatia.Matrix Analysis.Solutions to Exercises and Problems]ExI.4.5
Suppose it is known that $\scrM$ is an invariant subspace for $A$. What invariant subspaces for $A\otimes A$ can be obtained from this information alone?
Solution. It is $\scrM\otimes \scrM$ that is an invariant subspace of $A\otimes A$. Indeed, if $x,y\in M$, then $$\bex (A\otimes A)(x\otimes y)=(Ax)\otimes (Ay)\in M\otimes M. \eex$$
[Bhatia.Matrix Analysis.Solutions to Exercises and Problems]ExI.4.5的更多相关文章
- [Bhatia.Matrix Analysis.Solutions to Exercises and Problems]ExI.4.1
Let $x,y,z$ be linearly independent vectors in $\scrH$. Find a necessary and sufficient condition th ...
- [Bhatia.Matrix Analysis.Solutions to Exercises and Problems]ExI.3.7
For every matrix $A$, the matrix $$\bex \sex{\ba{cc} I&A\\ 0&I \ea} \eex$$ is invertible and ...
- [Bhatia.Matrix Analysis.Solutions to Exercises and Problems]ExI.5.10
Every $k\times k$ positive matrix $A=(a_{ij})$ can be realised as a Gram matrix, i.e., vectors $x_j$ ...
- [Bhatia.Matrix Analysis.Solutions to Exercises and Problems]ExI.5.5
Show that the inner product $$\bex \sef{x_1\vee \cdots \vee x_k,y_1\vee \cdots\vee y_k} \eex$$ is eq ...
- [Bhatia.Matrix Analysis.Solutions to Exercises and Problems]ExI.5.1
Show that the inner product $$\bex \sef{x_1\wedge \cdots \wedge x_k,y_1\wedge \cdots\wedge y_k} \eex ...
- [Bhatia.Matrix Analysis.Solutions to Exercises and Problems]ExI.4.6
Let $A$ and $B$ be two matrices (not necessarily of the same size). Relative to the lexicographicall ...
- [Bhatia.Matrix Analysis.Solutions to Exercises and Problems]ExI.4.4
(1). There is a natural isomorphism between the spaces $\scrH\otimes \scrH^*$ and $\scrL(\scrH,\scrK ...
- [Bhatia.Matrix Analysis.Solutions to Exercises and Problems]ExI.2.8
For any matrix $A$ the series $$\bex \exp A=I+A+\frac{A^2}{2!}+\cdots+\frac{A^n}{n!}+\cdots \eex$$ c ...
- [Bhatia.Matrix Analysis.Solutions to Exercises and Problems]ExI.2.7
The set of all invertible matrices is a dense open subset of the set of all $n\times n$ matrices. Th ...
- [Bhatia.Matrix Analysis.Solutions to Exercises and Problems]ExI.2.6
If $\sen{A}<1$, then $I-A$ is invertible, and $$\bex (I-A)^{-1}=I+A+A^2+\cdots, \eex$$ aa converg ...
随机推荐
- ajax,json和$.each()
json返回的时候,只需要展示部分字段,如果是 ajax从后台获取结果处理,可以使用.select() 等处理结合匿名类,生成需要的字段的匿名类json字符串,返回前端,可以使用$.parseJson ...
- storyboard 总结
1.storyboard 布局时用代码实现页面跳转: a> 获取当前 storyboard : [self storyboard] b> 为将要跳转到的 viewController 添加 ...
- 三年PS经验
- eclipse颜色配置
Eclipse颜色主题插件:Eclipse Color Theme http://blog.sina.com.cn/s/blog_674212810101go8x.html 一个很赞的eclipse插 ...
- 基于Oracle OCI的数据访问C语言接口ORADBI .
基于Oracle OCI的数据访问C语言接口ORADBI cheungmine@gmail.com Mar. 22, 2008 ORADBI是我在Oracle OCI(Oracle 调用接口)基础 ...
- PHP 怎么随机获取数组里面的值
注意array_rand随机返回的是KEY值的集合 <?php srand((float) microtime() * 10000000); $input = array("Neo&q ...
- Java 另一道构造器与构造器重载的题目
题目: 请写出以下程序的输出结果 public class ConstructorTest2 { public static void main(String[] args) { new B(&quo ...
- CentOS7.1配置远程桌面
网上看了很多资料,完全是乱的. 我使用的是CentOS7.1的系统.我的要求是windows的客户机可以远程访问CentOS系统. 1,首先需要检查一下服务器是否已经安装了VNC服务,检查服务器的是否 ...
- Java经典书籍
Java Web开发教程---孙霞JSP应用开发详解(第三版)---刘晓华.张健.周慧贞Spring in Action---Craig Walls精通Struts基于MVC的Java Web设计与开 ...
- SQL Server Mobile 和 .NET 数据访问接口之间的数据类型映射
.NET 数据类型 SQL Server Mobile 数据类型 binary varbinary boolean bit byte tinyint byte[] varbinary dateti ...