(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 p...
分类：
其他好文 时间：
2014-11-18 13:20:04
阅读次数：
211
Show that the following statements are equivalent:
(1). $A$ is positive.
分类：
其他好文 时间：
2014-11-18 13:17:56
阅读次数：
186
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 $A$. T...
分类：
其他好文 时间：
2014-11-18 13:14:41
阅读次数：
199
Show that matrices with distinct eigenvalues are dense in the space of all $n\times n$ matrices. (Use the Schur triangularisation)
分类：
其他好文 时间：
2014-11-18 13:12:08
阅读次数：
174
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 ...
分类：
其他好文 时间：
2014-11-18 13:09:44
阅读次数：
120
(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 e...
分类：
其他好文 时间：
2014-11-18 13:08:29
阅读次数：
168
For fixed basis of in $\scrH$ and $\scrK$, the matrix $A^*$ is the conjugate transpose of the matrix of $A$.
分类：
其他好文 时间：
2014-11-18 13:08:12
阅读次数：
195
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.
分类：
其他好文 时间：
2014-11-18 13:07:47
阅读次数：
151
Food Delivery
Time Limit: 2 Seconds Memory Limit: 65536 KB
When we are focusing on solving problems, we usually prefer to stay in front of computers rather than go out for lunch. At thi...
分类：
其他好文 时间：
2014-11-17 22:57:23
阅读次数：
529
在problems窗口可以看到错误信息
菜单栏 window--》show view--》problems
或alt+shift+q 然后按x
重新选一下包就解决了...
分类：
编程语言 时间：
2014-11-16 21:41:14
阅读次数：
341
