How to typedef a template class?
C++ template typedef
How can I check dependency list for a deb package How can I check dependency list for a deb package. I am running Ubuntu 11.10 and I have backed up all deb packages from var/cache/apt/archives. I want to format my pc and re-install selected applications only. Also how can I get the list of installed packages and dependencies. Possible to have the default landing page of my Sharepoint Site be an applicaiton page? So basically when someone goes to:   http://mysite.com   I would like to show an Application Page that I have created, without the giant URL.  Example of the giant URL :  http://mysite.com/_layouts/ap/myAppPage.aspx   Is there any way for me to do this? Let $V$ be an n-dimensional vector space over $\mathbb{R}$ and $T:V \rightarrow V$ be linear. Call a vector $v \in V$ cyclic if $V$ is spanned by $\{v, \ Tv, \ T^2v,..\}$.  Question:  Show that $v$ is cyclic for $T$ then there is some $k \geq 1$ such that   $$B=\{v, \ Tv,..T^{k-1}v \}$$ is linearly independent in $V$ and that $T^kv$ lies in  the span of $B$.  Thoughts:  If we suppose that no such $k$ exists, then every subset of the form $\{v, \ Tv,..T^{l-1}v \}$ is linearly dependent, or it is linearly dependent with $T^lv$ not lying in it span.  There are in effect then two cases to consider.  Suppose every subset of the form $\{v, \ Tv,..T^{l-1}v \}$ is linearly dependent. Then $T^{l-1}$ can be expressed as a linear combination of $v,...,T^{l-2}v$. Now, $\{v, \ Tv,..T^{l-2}v \}$ is also linearly dependent by assumption and so we can express $T^{l-2}$ as a linear combination of  $v,...,T^{l-3}v$ etc... Continuing in this way, we show that $T^{l-1}v= \lambda v$ for some $\lambda \in \mathbb{R}$. Thus $$B=\{ \mu v \ | \ \mu \ \text{is an eigenvalue of} \ T^mv \ \text{for some} \ m \}$$ This is 'at best' countably infinite, and therefore could not span $V$ even if it were 1-dimensional, wince our base field is $\mathbb{R}$, which is uncountable.  Suppose then that $B$ is linearly independent for some $k$ but that $T^kv$ does not lie in its span. I can't see how to progress this argument.  Note: This question is for second year Undergraduates, and I think there must be some more simple approach; even the first part surprises me if we need to argue using the uncountability of $\mathbb{R}$, so any alternative approaches are also appreciated. How do you get \mathbb{1} to work (characteristic function of a set)? is there a way to get the option "Organize Desktop by Name" in Ubuntu 19.10 same as in 18.04? the option in Ubuntu 18.04 is "Organize Desktop by name"    But there is no option available in Ubuntu 19.10 How to mount PCIe SSD from MacBook Air in another computer I got this SSD out of an Apple laptop that's broken from liquid damage.  What is this connection called and how do I mount this storage device to retrieve data from it? It looks like PCIe. Does Apple sell a part to mount this via USB adapter or something? Can we have a way to edit bounty custom message? Is there a constructive way to exhibit a basis for $\mathbb{R}^\mathbb{N}$? I go to change my birthdate on Roblox, but nothing shows up, the dropdowns are just blank with no Month, Day or Year:  It also shows me a pop up asking to put in the Missing Details to improve the experience, but no matter how many times I put in my age it doesn't save and asks it again. I am creating a chat using Ajax requests and I'm trying to get messages div to scroll to the bottom without much luck. I am wrapping everything in this div: #scroll {     height:400px;     overflow:scroll; }  Is there a way to keep it scrolled to the bottom by default using JS? Is there a way to keep it scrolled to the bottom after an ajax request? To find all $n$ such that $(n-1)!+1$ is a perfect power of $n$ How to find all positive integers $n$ such that $(n-1)!+1$ can be written as $n^k$ for some positive integer $k$? 'pyrcc5' is not recognized as an internal or external command The real fastest gun in the west Are the questions in the about page taken from real posts? If not, who designs them?  Particularly, why does this specific answer have a date from before the question was asked? Is it possible to run Snow Leopard on a LATE 2011 MacBook Pro? Local collection of Python packages: best way to import them? I downloaded and installed Ubuntu from the official site. However, I don't know if I installed the 32-bit or 64-bit version.  In Windows 7 I could right click My Computer and it listed which version it was.  Is there an easy way to check in Ubuntu? Can the Help action be used to give advantage to a specific ally's attack (rather than just the next ally who attacks the target)? Do I need internet/3G to use GPS? I have a Samsung Galaxy S2 that has some problems with the GPS: If I use internet my navigation works but when I turn the 3G off, GPS does not work.  Do I need internet/3G to use GPS? How to disable the skype ads (advertisement)? How to backup an Android device?