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

  1. [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 ...

  2. [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 ...

  3. [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 $x_j$ ...

  4. [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 ...

  5. [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 ...

  6. [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 ...

  7. [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 ...

  8. [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 ...

  9. [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 ...

  10. [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

  1. 【BZOJ 1054】 [HAOI2008]移动玩具

    Description 在一个4*4的方框内摆放了若干个相同的玩具,某人想将这些玩具重新摆放成为他心中理想的状态,规定移动时只能将玩具向上下左右四个方向移动,并且移动的位置不能有玩具,请你用最少的移动 ...

  2. 总有你需要的之 ios 小技巧 (下)

    图片上绘制文字 写一个UIImage的category NSMutableParagraphStyle* paragraphStyle = [[NSParagraphStyle defaultPara ...

  3. s3c2440之cache

    cache高速缓冲存储器注意与块设备页高速缓存进行区别,一个是硬件的实现一个是软件的实现,块设备页高速缓存. s3c2440/s3c2410里面主要有一个arm920t的核,但同时包含几个协处理器,协 ...

  4. Android架构图

  5. Otto Product Classification Winner's Interview: 2nd place, Alexander Guschin ¯\_(ツ)_/¯

    Otto Product Classification Winner's Interview: 2nd place, Alexander Guschin ¯\_(ツ)_/¯ The Otto Grou ...

  6. django 的mysql数据配置

    原地址:http://blog.csdn.net/gamesofsailing/article/details/21465327 在成功安装python-mysql后,开始配置django的mysql ...

  7. Unix/Linux下如何使用Vi编辑器

    vi 的工作模式 Vi 在初始启动后首先进入编辑模式,这时用户可以利用一些预先定义的按键来移动光标.删除文字. 复制或粘贴文字等.这些按键均是普通的字符,例如 l 是向右移动光标,相当于向右箭头键,k ...

  8. （转）eclipse快捷键

    Eclipse常用快捷键 Eclipse的编辑功能非常强大,掌握了Eclipse快捷键功能,能够大大提高开发效率.Eclipse中有如下一些和编辑相关的快捷键. 1. [ALT+/] 此快捷键为用户编 ...

  9. android dialog点击其他区域消失

    只需调用dialog对象的setCanceledOnTouchOutside方法,传入参数为true即可. 如下代码实现: //点击其他区域dialog消失 menuDialog.setCancele ...

  10. mysql学习链接

    1 传智播客PHP培训.刘道成.PHP视频教程.mysql http://down.51cto.com/zt/887