If $A_{n\times n}$ is nilpotent matrix then $\beta = (y, Ay,A^2y, \ldots, A^{k-1}y)$ is the basis of vector space $\mathbb R^n$.
Nilpotent matrix and basis for $F^n$
How do you collect valuable information from regular "User Group" meetings? The scenario:   You work on a SaAS application.  Some of your users use your application heavily each day. Every 2 weeks (or month or whatever), a "User Group" of your most avid users gets together to talk shop and see how their progress is going in the context of a larger project they are working on. You can participate and potentially direct some group activities aimed at improving the application.   How do you gather valuable user information in this group setting? I already have the pink and red leather gloves, the armor, the crown, and the monkey's staff (and they're all enchanted). Regardless of how many health potions I use, I always die. Help! compare two columns of different files and print if it matches I am using Solaris 10 and so grep options involving -f don't work.  I have two pipe-separated files:   file1:  abc|123|BNY|apple| cab|234|cyx|orange| def|kumar|pki|bird|   file 2:   abc|123| kumar|pki| cab|234   I would like to compare the first two columns of file2 with file1 (search through the entire contents of file1 in first two columns) if they match print the matched line of file1. Then search for the second line of file 2 and so on.   Expected Output:  abc|123|BNY|apple| cab|234|cyx|orange|   The files I have are huge, containing about 400,000 lines, so I would like to make the execution fast. Debugging errors of SAGA interpolation algorithms in QGIS Processing? I encounter recurrent problems with the geoalgorithms that perform interpolations. No matter what technique I use I end with the following errors. As stated in the OGR tab QGIS 2.0 is unable to open a file in C drive. I have very little IT background so the message error is meaningless.   Is there anybody able to decrypt the message and solve the problem?      here this is the algorithm i used How to get rid of the smell from the fridge? I just want to write a script which changes my directory.  I put the below commands in the file /home/alex/pathABC  #!/bin/sh cd /home/alex/Documents/A/B/C echo HelloWorld   I did   chmod +x pathABC   In the Terminal, while in /home/alex, I ran ./pathABC, but the output is just HelloWorld and the current directory is not changed.  So what is wrong? String formatting in Python I want to do something like String.Format("[{0}, {1}, {2}]", 1, 2, 3) which returns:  [1, 2, 3]   How do I do this in Python? Let $S = \bigoplus_{n\ge 0} S_n$ be a graded commutative ring. Let $f$ be a homogeneous element of $S$ of degree $&gt; 0$. Let $S_{(f)}$ be the degree $0$ part of the graded ring $S_f$, where $S_f$ is the localization with respect to the multiplicative set $\{1, f, f^2,\dots\}$. Suppose $S$ is finitely generated algebra over $S_0$. Then $S_{(f)}$ is a finitely generated algebra over $S_0$. Select all contents of textbox when it receives focus (Vanilla JS or jQuery) What is a Vanilla JS or jQuery solution that will select all of the contents of a textbox when the textbox receives focus? How to truncate milliseconds off of a .NET DateTime transpose columns to rows How to connect to my web server? Don't you think people need to know what they did wrong exactly so they can fix it and get unbanned from asking questions or posting answers? I am from Europe, and I did an internship in the US (California) in 2015. When filing my 2015 taxes, I ended up having to pay some small difference for the federal taxes, but got a refund on my state taxes, of roughly $1.6k. That was all the income I had in the US in 2016.  I did not enter the US in 2016 at all.  I managed to figure out that I don't need to file any California tax forms for 2016 (source: ) but I am not sure about federal taxes.  I tried researching the problem, and got some information on it, but the situation is still a bit unclear. It seems that since I listed my state tax as an itemized deduction in my 2015 tax report, which I filed in 2016, the state refund I got in 2016 is, in fact, taxable.  In this situation, would I have to file my taxes (and possibly pay owed tax) for 2016, even though I never set foot in the US in that year, and my total income is just $1.6k? How to distinguish Nexus 7 (2012) and Nexus 7 (2013) I am having trouble with Bluetooth Low Energy (BT 4.0) on a Nexus 7.  I think I may have a 2012 model.  How to tell if I have a 2012 or 2013 version of the Nexus 7? I recently upgraded to Snow Leopard, from Leopard and I was using an awesome app called  that let you remap your keys, set scripts/macros and even had repeat functionality.   However, this app doesn't seem to be in active development anymore, and 10.6 broke the ability to bind certain modifier keys (Shift) with other keys.   I totally miss things like Shift+Insert for paste (Linux/Windows), setting Ctrl+Shift+Esc for Activity Monitor, and Ctrl+Alt+Del for the login window.   So, how can I achieve this instead? A long time ago, I remember hiding some really personal files on my computer. Something that nobody could ever find, so I buried them down pretty darn good.  Now to my problem, I don't remember where.   Do anyone know a way to scan a drive and list all hidden folders and/or files?   I know how to view hidden files in Windows, but as far as I know, there is no way to search for them? I've been looking for a program, but I couldn't find one - and now I'm here, asking the experts. ;)  I'd really appreciate any tips. Using beamer \visible command inside a table, without adding vertical space When using the beamer \visible command inside a tabular environment, beamer adds an extra vertical space before the text. For example, in the following code, beamer adds an empty line before the word World in the second row. Can this be avoided?  \documentclass{beamer} \begin{document} \begin{frame}   \begin{tabular}{|p{1cm}|p{1cm}|}     \hline     1 &amp; Hello World \\     \hline     2 &amp; \visible&lt;2-&gt;{Hello World} \\     \hline   \end{tabular} \end{frame} \end{document} I tried to install Ubuntu 12.10 with the Wubi installer while running Windows, because my PC does not accept my BootCD as a bootable medium.  But Wubi showed me this error:  Ubuntu-Installationsprogramm (X) Ein Fehler ist aufgetreten: Could not retrieve the required disk image files Weiter Informationen finden Sie in der Protokolldatei: c:\users\username\appdata\local\temp\wubi-12.10-rev273.log   What can I do, because I want to get rid of my Windows 7 and use the way better Ubuntu 12.10?  Thanks for your huge answer, now my next problem after trying to install wubi with the .iso is, that the same error shows up again and i am not shure which part of the errorreport you need.  Can you tell me? Because i'm not that good at linux. How fast a (relatively) small black hole will consume the Earth? This question appeared quite a time ago and was inspired, of course, by all the fuss around "LHC will destroy the Earth".   Consider a small black hole, that is somehow got inside the Earth. Under "small" I mean small enough to not to destroy Earth instantaneously, but large enough to not to evaporate due to the . I need this because I want the black hole to "consume" the Earth. I think reasonable values for the mass would be $10^{15} - 10^{20}$ kilograms.   Also let us suppose that the black hole is at rest relative to the Earth.  The question is: How can one estimate the speed at which the matter would be consumed by the black hole in this circumstances?