I got this problem:  Is it true or not that for every matrix $A\in M_2( \mathbb C)$ there is a matrix $X\in M_2( \mathbb C)$ such that $X^2=A$? prove the answer.  I know that we can pass to Jordan form, and I proved that this claim is true for all the Jordan forms except  $$         \begin{pmatrix}         0 &amp; 1  \\         0 &amp; 0  \\         \end{pmatrix} $$ any suggestions what to do with this matrix? and also, there is a general version of this problem? thanks for helpers!
True\False?  For every matrix $A\in M_{2}( \mathbb{C}) $ there's  $X\in M_{2}( \mathbb{C})$ such that $X^2=A$.  I know that every complexed matrix has a Jordan form matrix $J$ such that $P^{-1}CP=J$, But it's not diagonalizable for sure.  Thanks
I am looking at collecting spatial information from a range of stakeholders to identify opportunities within a landscape.  However, the data that we are collecting are not presently mapped and so we wish to use an interactive method to get this information onto a map.  Which online websites/methods would people recommend for circulating to a non-technical audience to try and get them to map what they know?    Where the emphasis is on ease of use by the stakeholder. Is there an easy way to put a box around a theorem in LaTeX? For example to state an important theorem. I tried using page 20 of the ntheorem , but I do not know how to use the package. meaning of the word "in" in context It is from . It is at around 8 minute and 39 second. Here it goes:     Culinary cultural fusion is all the rage; more novels translated from languages then ever before, although few are read, and in the surest sign of cultural globalization, football, the world's game, finally has reached America.   I guess the sentence would make sense if the preposition in were dropped out. Could you please tell me what did the host use it for? Does a percentage quantity take singular or plural verb agreement? Does a percentage require a singular or plural verb, for example, do we say ten percent "go" or "goes"? I need to include a couple of Python code listings, where the indentation of the lines (using some number of spaces) is significant. I would like for the code listings to be copyable, so the spaces at the beginning of the line need to be be copied along with the text.  This question has been asked in various ways before (e.g. , or ). Those questions focus on making line numbers uncopyable, though.  Making the spaces at the beginning of a line copyable seems to be harder: "I am not sure it is possible to specify in the PDF (at least in a viewer-independent way) that the indentation should be copied too" (). At , Philippe Goutet suggests a solution (turning the spaces into visible spaces, and coloring them in the background color so that they appear invisible) that works using Acrobat Reader, but not all readers. He says "It works under Acrobat Reader and it's extremely pleasant to be able to quickly copy/paste code without problem (perhaps the problem can be circumvented by writing direct PDF code to tell that it's a space, I've never had the time to try)".  Is it possible to produce a PDF with a code listing with copyable real spaces at the beginning of a line?  Minimal example: The line return x should start with four spaces.  \documentclass{article}  \begin{document} \begin{verbatim} def myfunction(x):     return x \end{verbatim} \end{document}   I know that I could attach the code to the PDF as a file, but that's not what I want. Accessing localhost (xampp) from another computer over LAN network - how to? I have just set up a wi-fi network at home. I have all my files on my desktop computer (192.168.1.56) and want to access localhost over there from another computer (192.168.1.2).  On my desktop I can access localhost through the normal . Apache is running on port 80 as usual.  Exactly what do I have to do to achieve this? There is documentation on the net but they either don't work or are too fragment and confusing to understand.  I think I have to make changes to my apache's httpd.conf file and the hosts file. Any ideas as to what changes to make? How to make sure an application keeps running on Linux I'm trying to ensure a script remains running on a development server. It collates stats and provides a web service so it's supposed to persist, yet a few times a day, it dies off for unknown reasons. When we notice we just launch it again, but it's a pain in the rear and some users don't have permission (or the knowhow) to launch it up.  The programmer in me wants to spend a few hours getting to the bottom of the problem but the busy person in me thinks there must be an easy way to detect if an app is not running, and launch it again.  I know I could cron-script ps through grep:  ps -A | grep appname   But again, that's another hour of my life wasted on doing something that must already exist... Is there not a pre-made app that I can pass an executable (optionally with arguments) and that will keep a process running indefinitely?  In case it makes any difference, it's Ubuntu. We have to prove that  "the product of two numbers ending in 6 also ends with 6" mathematically.  I have no clue how to start. I don't want you to prove it for me! but some hints would be very helpful as I'm totally stuck on how to start this prove. $M$ connected $\iff$ $M$ and $\emptyset$ are the only subsets of $M$ open and closed at the same time I'm trying to understand this proof that:  $M$ connected $\iff$ $M$ and $\emptyset$ are the only subsets of $M$ open and closed at the same time  Which is:  If $M=A\cup B$ is a separation, then $A$ and $B$ are open and closed. Recriprocally, if $A\subset M$ is open and closed, then $M = A\cup(M-A)$. What? I know that if $M=A\cup B$ is a separation, $A$ and $B$ are both open. But why closed? Also, the 'recriprocally' part is totally nonsense to me. Anybody could help?  Also, there's another proof, which states: $M$ and $\emptyset$ are the only subsets of $M$ at the same time closed and open $\iff$ if $X\subset M$ has empty boundary, theb $X=M$ or $X=\emptyset$  which is proved as the following:  given $X\subset M$, we know the condition $X\cap \partial X = \emptyset$ implies $X$ is open, while the condition $\partial X \subset X$ implies $X$ is closed. Then, $X$ is open and closed $\iff$ $\partial X = X\cap \partial X = \emptyset$, this show $\iff$ for the theorem above.  First of all, I think that the condition $X$ has boundary empty implies that $X\cap \partial X$ is empty, but who said anything about $\partial X\subset X$? Also, where's the $\rightarrow$ of this proof? I can only see $\leftarrow$ I am making a Dwarf Warpriest Cleric of Shelyn wielding a Glaive. I expect to use Medium armor. I am planning this character out through level 20.   I'm looking for a build of feats, skills (if applicable) and spells that maximize my damage in melee and healing with spells. Other character choices are locked in.  If it matters, my allies in this group are: rogue, sorcerer, barbarian, monk, and fighter(longbow).   My original plan includes:    (Zeal Domain)     What Feats, Skills, and Spells (through level 20) will allow this character to do its highest DPR with a glaive and heal the most with its spell slots? I can show this best by a picture:    This cross also shows when I export it as raster or pdf. What is it and how can I get rid of it?  I am using Qgis 2.4 and the map was done with the help of the Grass plugin AniMove on Linux Mint. Ever since I upgraded to 15.10, fdisk -l reports 16 ram disks (/dev/ram0 ... /dev/ram15). I'm a bit unsure what those are needed for. Is it safe to delete them? If not, how can I get rid of that fdisk output? I have created a VF page and used "render as pdf"  &lt;apex:commandButton value="Save to Opportunity" action="{!savePdf}"  /&gt;   Its working fine when i am using above line without rerender and oncomplete but when i am adding rerender or oncomplete it is not working.I am able to save the PDF in attachment folder but when i am trying to open its showing  "Unable to load document"  Even if i remove oncomplete and use Rerender then also its saving the attachment in Attachment object and when i view ,it is not loading and says "Unable to load document"      &lt;apex:commandButton value="Save to Opportunity" action="{!savePdf}"  oncomplete="myClose();"/&gt;   Javascript Code  function myClose(){      self.close();     window.opener.location.href="/{!$CurrentPage.parameters.Id}";  }   Class Code  public void savePdf() {      PageReference pdf = Page.GenerateQuotePDF;     pdf.getParameters().put('id',parentId);      Attachment attach = new Attachment();      Blob body;     body = pdf.getContent();     attach.Body = body;     attach.Name = 'Opportunity'+ '.pdf';       attach.IsPrivate = false;     attach.ParentId = parentId;     attach.ContentType = 'application/pdf';     insert attach;     }     Please help.. Why shouldn't I mix tabs and spaces? Solving SDE: $dX(t) = udt + \sigma X(t)dB(t)$ understanding "mount" as a concept in the OS I want to understand what mounting is. It is used in different contexts and situations and I can't find resources which:   Describe the mount concept Explain the actions taken by the computer/OS/utility when a mount is performed How and in which situations mount is used Which features in the Linux mount command are of frequent use and some examples   ( I hear mount applied to diverse entities directories, flash drives, network card, etc ) Can Xcode 6 and Xcode 5 coexist on the same computer? I found the .bashrc file and I want to know the purpose/function of it. Also how and when is it used? Why does Gandhi want to nuke me? Different civilizations obviously have different priorities. For example, Gandhi always seems to rush nuke technology and the Mongols will most likely start invading and spread like mad. Are these variables public knowledge? Can you tell by who you are playing what strategy they will adopt during the game? Synchronize Clocks I need to develop a system where there are 4 sensor boxes powered by USB and they have their internal clock. Each of these boxes are connected to a Linux pc and all these PCs are linked with WiFi. API of the sensor box allows me to read their internal precision clock (uSec accuracy).   I like to synchronize all four clocks of the sensor boxes as close as possible. Hopefully within a few micro seconds of each other and compensate for drift over time. The idea is to use the sensor data that is collected at the same time (The data I receive is time stamped with the boxes' internal clock). The latency on usb bus, WiFi, pc timing are all indeterministic.  Is this possible given my setup?