[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 $x_j$, $1\leq j\leq k$, can be found so that $a_{ij}=\sef{x_i,x_j}$ for all $i,j$.
Solution. By Exercise I.2.2, $A=B^*B$ for some $B$. Let $$\bex B=(x_1,\cdots,x_k). \eex$$ Then $$\bex A=\sex{\sef{x_i,x_j}}. \eex$$
[Bhatia.Matrix Analysis.Solutions to Exercises and Problems]ExI.5.10的更多相关文章
- [Bhatia.Matrix Analysis.Solutions to Exercises and Problems]ExI.2.10
(1). The numerical radius defines a norm on $\scrL(\scrH)$. (2). $w(UAU^*)=w(A)$ for all $U\in \U(n) ...
- [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.5.5
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 ...
随机推荐
- 2016 系统设计第一期 （档案一）MVC form数据提交
前几天我发现 MVC 虽然解决了webform的问题但是用起来真的很麻烦,不知道是我刚接触的原因还是为什么,感觉有很多的局限性,对于form的提交一个form只能绑定一个action,代码如下: @u ...
- 【BZOJ 2654】tree
Description 给你一个无向带权连通图,每条边是黑色或白色.让你求一棵最小权的恰好有need条白色边的生成树. 题目保证有解. Input 第一行V,E,need分别表示点数,边数和需要的白色 ...
- linux du 与 df 命令
du 命令:显示每个文件和目录的磁盘使用空间 命令格式:du [选项][文件] -k或--kilobytes 以KB(1024bytes)为单位输出. -m或--megabytes 以MB为单位输 ...
- ubuntu下安装GTK过程
GTK的安装过程比较繁琐,以前也安装过,但没有记录下来,Google一下记录下来备用. 利用此方法成功在ubuntu12.04下安装GTK 2.24.10 1.安装gcc/g++/gdb/make 等 ...
- 使用Yeoman搭建 AngularJS 应用 (9) —— 让我们搭建一个网页应用
原文地址:http://yeoman.io/codelab/install-packages.html 列出当前程序包 我们现在查看一下我们已经安装的程序包,输入下面的命令 bower list 查找 ...
- [DP] 堆盒子问题
给一堆盒子,知道每个盒子的三围(长宽高),盒子正面朝你,不能旋转摆放,按照大的放在小的下面的原则堆起来,必须是 strictly larger,同样大小的盒子不行,问怎么样堆到最大的高度? 思路:动态 ...
- 深入js的面向对象学习篇——温故知新（一）
在学习设计模式前必须要知道和掌握的***. 为类添加新方法: Function.prototype.method = function(name,fn) { this.prototype[name] ...
- select框的text与value值的获取(实用版)
function def(){ var key = document.getElementById ('selectarea'); //select list var value = docum ...
- WPF 位置转化和动画
位置转化 private void DrawScale() { double majorTickUnitValue = this.ScaleSweepLenth / this.MajorDivisio ...
- FireFly 服务端 Unity3D黑暗世界 客户端 问题
启动服务端成功截图: 连接成功截图: 测试服务端是否启动成功: 在Web输入:http://localhost:11009/ 按回车 (查看cmd启动的服务端 是否多出如下显示) 服务端启动成功.P ...