EXI

打开外部文件的几种 语法， openFile [ mode: ]

  r - read-only text - file must exi
·2015-11-12 23:54

第一篇！in和exists性能比较和使用

正确的应该是： 　　　　①如果查询的两个表大小相当，那么用in和exists差别不大； 　　　　②如果两个表中一个较小，一个是大表，则子查询表大的用exi
·2015-11-12 22:36

asp.net word内容读取到页面

ReadWordFile(string file) { string filePath = Server.MapPath(file); if (System.IO.File.Exi
·2015-11-12 20:16

PL/SQL — 集合及常用方法

一、集合类型提供的方法与调用方式 1、集合的方法与调用方式 EXISTS 函数EXI
·2015-11-12 18:08

Find Minimum in Rotated Sorted Array

You may assume no duplicate exi
·2015-11-12 10:13

Find Minimum in Rotated Sorted Array

You may assume no duplicate exi
·2015-11-11 10:00

在Sql Server触发器中判断操作是Insert还是Update还是Delete

SELECT 1 FROM deleted)SET @IsInsert = 1ELSESET @IsInsert = 0 IF EXISTS(SELECT 1 FROM inserted) AND EXI
·2015-11-11 09:35

PetaPoco与MySQL

  查询业务 public class BaseViewModel { #region Create DataBase, if not exi
·2015-11-11 08:15

Find Minimum in Rotated Sorted Array——LeetCode

You may assume no duplicate exi
·2015-11-11 01:34

注意:php5.4删除了session_unregister函数

php //php5.4删除了session_unregister函数 //by www.jbxue.com function exi
·2015-11-10 23:18

【LeetCode】58. Length of Last Word

If the last word does not exi
·2015-11-08 11:04

按需路由原理 (ODR-On Demand Routing)

RouterAenconftints0/0clockrate64000ipadd12.1.1.1255.255.255.0noshutintlo0ipadd172.16.1.1255.255.255.0exi
kid716·2015-11-06 23:37

Realm Configuration HOW-TO--官方

document describes how to configure Tomcat to support container managed security, by connecting to an exi
·2015-11-02 16:29

[LeetCode] Find Minimum in Rotated Sorted Array 二分搜索

You may assume no duplicate exi
·2015-11-01 14:01

【Linux 编程】vfork

在子进程调用exec或exi
·2015-11-01 09:53

Gentoo rc-update service ‘net.eth0′ does not exist

nano -w /etc/conf.d/net # rc-update add net.eth0 default rc-update service ‘net.eth0′ does not exi
·2015-10-31 17:37

leetcode[153]Find Minimum in Rotated Sorted Array

You may assume no duplicate exi
·2015-10-31 10:58

winform程序的关闭

如果在form1中使用application.exi
·2015-10-31 09:44

[LeetCode] Find Minimum in Rotated Sorted Array

You may assume no duplicate exi
·2015-10-30 14:27

【leetcode刷题笔记】Find Minimum in Rotated Sorted Array

You may assume no duplicate exi
·2015-10-30 13:14

OBJECTPROPERTY与sp_rename更改对象名称

 实例一，更改表名： View Code IF  EXI
·2015-10-30 12:17

Only one expression can be specified in the select list when the subquery is not introduced with EXI

/*错误的*/ select song.song_name,song.title_url,song.mv_url,singer.singer_name from WEBDB_PROD_SONG as song, WEBDB_PROD_SINGER as singer where song.singer_id=singer.singer_id and song.song_name=(select
·2015-10-27 15:57

执行一条cmd命令的window.bat 批处理代码：

supervisor d:\WWWBOX\LEAPNODE\server.js ::暂停 3 秒时间 ping -n 3 127.0.0.1 > nul ::暂停 ::pause Exi
·2015-10-23 08:55

winform程序的关闭

如果在form1中使用application.exi
·2015-10-21 12:26

[Bhatia.Matrix Analysis.Solutions to Exercises and Problems]ExI.5.3

Let $\scrM$ be a $p$-dimensional subspace of $\scrH$ and $\scrN$ its orthogonal complement. Choosing $j$ vectors from $\scrM$ and $k-j$ vectors from $\scrN$ and forming the linear span of the antisymm
·2015-10-21 11:32

[Bhatia.Matrix Analysis.Solutions to Exercises and Problems]ExI.5.2

The elementary tensors $x\otimes \cdots \otimes x$, with all factors equal, are all in the subspace $\vee^k\scrH$. Do they span it?   Solution. Yes. Indeed, take $$\beex \bea &\quad (x+y)\o
·2015-10-21 11:30

[Bhatia.Matrix Analysis.Solutions to Exercises and Problems]ExI.5.1

Show that the inner product $$\bex \sef{x_1\wedge \cdots \wedge x_k,y_1\wedge \cdots\wedge y_k} \eex$$ is equal to the determinant of the $k\times k$ matrix $\sex{\sef{x_i,y_j}}$.   Solution. $
·2015-10-21 11:30

[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 $\scrM\otimes \scrM$
·2015-10-21 11:29

[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 lexicographically ordered basis on the space of tensors, the matrix for $A\otimes B$ can be written in block form as
·2015-10-21 11:29

[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 that a vector $w$ mush satisfy in order that the bilinear functional $$\bex F(u,v)=\sef{x,u}\sef{y,v}+
·2015-10-21 11:27

[Bhatia.Matrix Analysis.Solutions to Exercises and Problems]ExI.4.4

(1). There is a natural isomorphism between the spaces $\scrH\otimes \scrH^*$ and $\scrL(\scrH,\scrK)$ in which the elementary tensor $k\otimes h^*$corresponds to the linear map that takes a vector $u
·2015-10-21 11:27

[Bhatia.Matrix Analysis.Solutions to Exercises and Problems]ExI.3.1

Let $A=A_1\oplus A_2$. Show that   (1). $W(A)$ is the convex hull of $W(A_1)$ and $W(A_2)$; i.e., the smallest convex set containing $W(A_1)\cup W(A_2)$.   (2). $$\beex \bea \sen{A}&
·2015-10-21 11:25

[Bhatia.Matrix Analysis.Solutions to Exercises and Problems]ExI.3.6

If $A$ is a contraction, show that $$\bex A^*(I-AA^*)^{1/2}=(I-A^*A)^{1/2}A^*. \eex$$ Use this to show that if $A$ is a contraction on $\scrH$, then the operators $$\bex U=\sex{\ba{cc} A&(I-AA^*)^
·2015-10-21 11:25

[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 its inverse is $$\bex \sex{\ba{cc} I&-A\\ 0&I \ea}. \eex$$ Use this to show that if $A,B$ a
·2015-10-21 11:25

[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. The set of all unitary matrices is a compact subset of all $n\times n$ matrices. These two sets are al
·2015-10-21 11:24

[Bhatia.Matrix Analysis.Solutions to Exercises and Problems]ExI.2.8

For any matrix $A$ the series $$\bex \exp A=I+A+\frac{A^2}{2!}+\cdots+\frac{A^n}{n!}+\cdots \eex$$ converges. This is called the exponential of $A$. The matrix $A$ is always invertible and $$\bex (\ex
·2015-10-21 11:24

[Bhatia.Matrix Analysis.Solutions to Exercises and Problems]ExI.2.9

(1). When $A$ is normal, the set $W(A)$ is the convex hull of the eigenvalues of $A$. For nonnormal matrices, $W(A)$ may be bigger than the convex hull of its eigenvalues. For Hermitian operators, the
·2015-10-21 11:24

[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 $U\in \U(n)$.   (3). $w(A)\leq \sen{A}\leq 2w(A)$ for all $A$.   (4). $w(A)=\sen{A}$ if
·2015-10-21 11:24

[Bhatia.Matrix Analysis.Solutions to Exercises and Problems]ExI.2.5

Show that matrices with distinct eigenvalues are dense in the space of all $n\times n$ matrices. (Use the Schur triangularisation)   Solution.  By the Schur triangularisation, for each mat
·2015-10-21 11:22

[Bhatia.Matrix Analysis.Solutions to Exercises and Problems]ExI.2.4

(1). The singular value decomposition leads tot eh polar decomposition: Every operator $A$ can be written as $A=UP$, where $U$ is unitary and $P$ is positive. In this decomposition the positive part $
·2015-10-21 11:22

[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 convergent power series. This is called the Neumann series.   Solution.  Since $\sen{A}<1$,
·2015-10-21 11:22

[Bhatia.Matrix Analysis.Solutions to Exercises and Problems]ExI.2.2

Show that the following statements are equivalent: (1). $A$ is positive. (2). $A=B^*B$ for some $B$. (3). $A=T^*T$ for some upper triangular $T$. (4). $A=T^*T$ for some upper triangular $T$ with n
·2015-10-21 11:21

[Bhatia.Matrix Analysis.Solutions to Exercises and Problems]ExI.2.3

(1). Let $\sed{A_\al}$ be a family of mutually commuting operators. Then, there exists a common Schur basis for $\sed{A_\al}$. In other words, there exists a unitary $Q$ such that $Q^*A_\al Q$ is uppe
·2015-10-21 11:21

[Bhatia.Matrix Analysis.Solutions to Exercises and Problems]ExI.2.1

For fixed basis of in $\scrH$ and $\scrK$, the matrix $A^*$ is the conjugate transpose of the matrix of $A$.   Solution.  $$\beex \bea (A^*)_{ij}&=e_i^*A^*f_j\\ &=\sef{e_i,A^*f_j}_
·2015-10-21 11:20

[Bhatia.Matrix Analysis.Solutions to Exercises and Problems]ExI.1.3

Use the QR decomposition to prove Hadamard's inequality: if $X=(x_1,\cdots,x_n)$, then $$\bex |\det X|\leq \prod_{j=1}^n \sen{x_j}. \eex$$ Equality holds here if and only if the $x_j$ are mutually ort
·2015-10-21 11:19

[Bhatia.Matrix Analysis.Solutions to Exercises and Problems]ExI.1.2

Let $X$ be nay basis of $\scrH$ and let $Y$ be the basis biorthogonal to it. Using matrix multiplication, $X$ gives a linear transformation from $\bbC^n$ to $\scrH$. The inverse of this is given by $Y
·2015-10-21 11:19

[Bhatia.Matrix Analysis.Solutions to Exercises and Problems]ExI.1.1

Given any $k$-tupel of linearly independent vectors $X$ as above, there exists a $k$-tuple $Y$ biorthognal to it. If $k=n$, this $Y$ is unique.   解答: Since $$\bex \rank(X^*X)=\rank(X)=k, \eex$$
·2015-10-21 11:18

[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
·2015-10-21 11:15

[Bhatia.Matrix Analysis.Solutions to Exercises and Problems]ExI.5.6

Let $A$ be a nilpotent operator. Show how to obtain, from aJordan basis for $A$, aJordan basis of $\wedge^2A$.   Solution. Since $A$ is nilpotent, each eigenvalue of $A$ is zero, and thus there
·2015-10-21 11:14

[Bhatia.Matrix Analysis.Solutions to Exercises and Problems]ExI.5.8

Prove that for any matrices $A,B$ we have $$\bex |\per (AB)|^2\leq \per (AA^*)\cdot \per (B^*B). \eex$$ (The corresponding relation for determinants is an easy equality.)   Solution. Let $$\bex
·2015-10-21 11:14
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