setting all elements of string array to one fixed length
How can I pad an integer with zeros on the left?
Prove that $T$ is an orthogonal projection Let $T$ be a linear operator on a finite-dimensional inner product space $V$. Suppose that $T$ is a projection such that $\|T(x)\| \le \|x\|$ for $x \in V$. Prove that $T$ is an orthogonal projection.    I can't understand well. The definition of orthogonal operator is $\|T(x)\| = \|x\|$. But why that $\|T(x)\| \le \|x\|$ for $x \in V$ means orthogonal projection? Why do clocks measure arc-length? When doing an apt-get update/upgrade I see that warning  W: Conflicting distribution: https://downloads.plex.tv/repo/deb public InRelease (expected public but got )   I was upgrading to Ubuntu Zesty 17.04 before and do not know how to fix the above. Already have seen ? but there are no suggested fixes for that.  Maybe one of you can give some hints? Thanks! Can't install aircrack-ng Whenever I attempt to install aircrack-ng in terminal I get the following error:  Package aircrack-ng is not available, but is referred to by another package. This may mean that the package is missing, has been obsoleted, or is only available from another source However the following packages replace it:   iw  E: Package 'aircrack-ng' has no installation candidate"   I'm new to Ubuntu and so have no idea what to do. I am using extensively trigonometric functions when an angle is given in degrees. Some of these functions like sine or cosine have rational values, for example, the well   known example is that $\cos(\theta) =0.6 $ and $\sin(\theta) =0.8 $.       However besides the case of multiplicity of $90^\circ$ it seems there are no rational numbers $\theta$  with simultaneously rational  values of  sine and cosine.      Is it possible somehow to prove that for rational values of an angle given in degrees there are  no values simultaneously rational of sine and cosine functions, beside obvious case of multiplicities of $90^\circ$? What happens with excess items if my bag is full, and what should I do to avoid losing items? There's a default limit of 350 items in the bag (even though you can expand it through the shop). I am currently level 6 and have already ~250 items in my bag. I haven't done any battles yet, as all the gyms in my area are too strong for my pokémon at the moment. So I have a lot of Pokéballs, Heals and Revives that I don't need right now.  What happens once my bag is full? Will additional items go into a temporary overflow bag? Will I just lose them? Will they replace older items?  I'm afraid I will lose the valuable items gained through a level-up. Should I throw away items to avoid that? If so, what should I throw out first? Heals and Revives, as I don't need them right now? Or will they become too valuable later on and I should rather throw out some Pokéballs as those are the most common items to receive from a Pokéstop?  TL;DR: What happens with items that exceed my bag size limit and what is the best strategy to avoid losing valuable items? Rotation and translation of a conic-section I tried to solve the following exercises, so I want to ask you if my answers are correct.     1) Given the coordinates system $(O'; X'' Y'')$ asociated to the    basis $B=[{b_1=\frac{1}{\sqrt{2}}; \frac{1}{\sqrt{2}};  &gt; b_2=\frac{-1}{\sqrt{2}}; \frac{1}{\sqrt{2}}}]$ with origin in    $O'=(2;5)$ and the system $(O;XY)$ asociated to the standar basis, find the intersection between $Q: y''^2=-4 \sqrt{2} x''$    and the straight line in $(O,XY)$ $V=(0;5)+t(-1;1) t\epsilon R$    Well, first I tried to write $Q$ in terms of $X$ and $Y$, and not in terms of $X''$ and $Y''$. I used the formula:  $(\begin{matrix}  X''\\  Y'' \\  \end{matrix})$ =$(C)_B$ × $(\begin{matrix}  X-2\\  Y-5 \\  \end{matrix})$   Then I replaced those values in the equation of $Q$ and I got $Q: \frac{(-x+y-3)^2}{2}=-4 \sqrt{2} \frac{(x+y-7)}{\sqrt{2}}$   After that, I found the intersection between $Q$ and $V$ using equations and I got that the intersection points in $(O;XY)$ are $P_1(3;2)$ and $P_2(-1;6)$      2)Given the coordinates system $(O,X'Y')$ asociated to the basis    $B=[{b_1=\frac{1}{\sqrt{2}}; \frac{1}{\sqrt{2}};  &gt; b_2=\frac{-1}{\sqrt{2}}; \frac{1}{\sqrt{2}}}]$ with origin in    $O=(0;0)$ and the ellipse $9X'^2+5Y'^2-3X'+2Y'-10=0$ find the    coordinates of the centre of the ellipse in $(O,XY)$    So, here I found the centre of the ellipse in $(O,X'Y')$ and it was $(\frac{1}{6}; - \frac{1}{5})$, then, doing something similar to what I've done before I found out that the centre in $(O,XY)$ was $( \frac{11}{30 \sqrt{2}};$ $\frac{-1}{30 \sqrt{2}}$) How do I fix a puncture? I got a flat/puncture on my bike tube, how can I fix it myself without going to the nearest bike shop? What kind of equipment would I need? Currently selected indicator's colour in flag summary and help pages, can be the same as the site's colour code Some of the Stack Exchange sites has it's own colour code. Like Meta Stack Exchange has #17a7db, ELU has #AE3737, Travel has #277789 for the currently selected item's indicators in main page and the user activity page. But in the flag summary section and help pages of those sites, the indicator has the colour of #F48024 which is same as the Stack Overflow site's colour code. So instead of applying the Stack Overflow's colour code to all the sites, shall we apply the site's specific colour code in flag summary and help pages too. Selected indicator in flag summary section of MSE, ELU and Travel:      Selected indicator in help page: Is the sorting algorithm used by .NET's `Array.Sort()` method a stable algorithm? Is the sorting algorithm used by .NET's Array.Sort() method a  algorithm? Proof verification: column rank = row rank $\newcommand{\span}{\operatorname{span}}\newcommand{\rank}{\operatorname{rank}}$I would like to prove that for every martix, column rank = row rank Let $A\in M_{m\times n}$ be some matrix. fix $R_A$ = vector space of the rows of $A$ , $C_A$ = vector space of the columns of $A$  $$\rank (R_A) = dim \ (\span \{R_1, R_2, \ldots, R_m\})$$ $$\rank (C_A) = dim \ (\span \{C_1, C_2, \ldots, C_n\})$$  let $x$ be some vector. $$x\in \operatorname{Null}(A) \Leftrightarrow \forall i  \ \ (1 \leq i \leq m) : \langle x,R_i\rangle = 0$$ (to be clear - I'm referring to the inner product of $x$ with each row of $A$) Using the rank nullity theorem, $\dim \operatorname{Null}(A) =  n - \rank(R_A)$ as $n$ =  number of columns. what I would like to do is to say: $$\dim \operatorname{Null}(A) =  n - \rank(R_A)$$ $$\dim \operatorname{Null}(A) = n - \rank(C_A)$$ therefore,  $\dim \operatorname{Null}(A) = n - \rank(R_A)= n - \rank(C_A)  \Longrightarrow \rank(R_A) = \rank(C_A) $ it that false? is using the rank- nullity  theorem this way is cheating? or just doesn't prove what needs to be proven formally? How do I pass a function as a parameter to in elisp? I'm trying to pass one method to another in elisp, and then have that method execute it.  Here is an example:  (defun t1 ()   "t1")  (defun t2 ()   "t1")  (defun call-t (t)   ; how do I execute "t"?   (t))  ; How do I pass in method reference? (call-t 't1) Upon the risk of being down voted as no MWE is present, but at the moment just trying to get some pointers. I updated my MiKTeX installation to the newest available version at the moment (MiKTeX-pdfTeX 4.1 (MiKTeX 20.12)) and now I get an error while building my documentation: Appendix D. (../html/examples/group/latex/refman_doc.tex (../html/examples/group/latex//gro up__group1.tex) [243] ! I can't write on file `../html/examples/group/latex//group__group2.aux'. \@include ...mmediate \openout \@partaux &quot;#1.aux&quot;                                                   \immediate \write \@partau... l.3 \include{group__group2}  Please type another output file name ! Emergency stop. \@include ...mmediate \openout \@partaux &quot;#1.aux&quot;                                                   \immediate \write \@partau... l.3 \include{group__group2}  *** (job aborted, file error in nonstop mode)  some small background:  Started normally with pdflatex doxygen_manual.tex in here is the statement: \subinputfrom{../html/examples/group/latex/}{refman_doc} and in this file again: \include{group__group2} as far as I know the disk is not full and the protections of the files and directories are OK as well  It looks like that now an attempt is made to write to the directory ../html/examples/group/latex/ whilst in the past the file was written to the current directory. I already tried -shell-escape and -enable-write18 (as well as --shell-escape and --enable-write18) but to no avail.  Any known changes in respect to writing the aux file? Any hints  edit I asked another question () with the details and MWE but that was closed with the reason that it was a duplicate of this one ... So I'm adding the information now here: In the question  asked about the problems I encountered due to an update of my MiKTeX distribution, but didn't take the time (at that moment) to create a MWE, so it didn't attract much response. I have the directory structure:  main  manual.tex   group  group__group2.tex refman_doc.tex    manual.tex \documentclass{book} \usepackage{import} \usepackage{hyperref}  \begin{document} \subinputfrom{../group}{refman_doc} \end{document}  group__group2.tex \hypertarget{group__group2}{}{The Second Group}  refman_doc.tex {Module Documentation} \include{group__group2}  When running in the directory main the command pdflatex manual.tex I get the error: ... (../group/../group/refman_doc.tex [1{C:/Users/User/AppData/Local/MiKTeX/2.9/pdf tex/config/pdftex.map}] ! I can't write on file `../group//group__group2.aux'. \@include ...mmediate \openout \@partaux &quot;#1.aux&quot;                                                   \immediate \write \@partau... l.2 \include{group__group2}  Please type another output file name:  but in a non interactive mode (the usual way to run. i.e. with \batchmode) one doesn't get an opportunity to specify the file and the generation crashes. As written in the original question adding options like -shell-escape and / or -enable-write18 didn't help.  Is there a solution for this problem?  edit 2 I did some further test. I replaced the \subinputfrom with an \input statement, although this worked for the limited example above it didn't work for my larger codebase as here (again just a limited view) we have in the refman_doc.tex {Module Documentation} \input{group__group1} \include{group__group2}  with the contents of group_group1.tex similar to group__group2.tex and the file is also parallel to group__group2.tex. This results in the error: (manual.out) (manual.out) (../group/refman_doc.tex  ! LaTeX Error: File `group__group1.tex' not found.  Type X to quit or &lt;RETURN&gt; to proceed, or enter new name. (Default extension: tex)  Enter file name: ! Emergency stop. &lt;read *&gt;  l.2 \input{group__group1}  !  ==&gt; Fatal error occurred, no output PDF file produced! Chapter on the right side - How to turn it off? Footnote in tabular environment Cortana Search is not finding applications on Windows 10 For the past several versions (since Windows Vista, I think), if you hit the Windows key and start typing, Windows will search for applications.  Since upgrading to Windows 10 with , she is only hit or miss at finding applications. And she doesn't do partial searches, either.  Some examples:   WinKey + type "Paint" does not find "mspaint". Instead it suggests some applications from the store. WinKey + type "Excel" does not find Excel. Nor does typing "Word" find Word. However, typing OneNote finds OneNote.   What is the reason for this behavior and how I can get Cortana to find the applications installed on my machine again? Is there a setting I am missing?    If I browse to "C:\ProgramData\Microsoft\Windows\Start Menu\Programs" I can see that the shortcuts for these applications all still exist. But Cortana is not finding them. Everything from the Microsoft Office applications to  to  to hundreds of other applications I have installed.  Where can I set which folders Cortana indexes?    As you can see in the screen shot below, this Start Menu folder is, indeed, indexed:    However, none of these applications are coming back as search results from the "start" menu.  It may be related to  as well.  I did a brand new install of Skype (for desktop), and it shows up nowhere in the start menu. And typing in "Skype" to search for the application does not find it. But the shortcut to Skype is definitely in this location:  C:\Users\Patrick\AppData\Roaming\Microsoft\Windows\Start Menu\Programs\Skype     EDIT  The latest Windows 10 update (Threshold 2) has solved this issue for me. Cortana now finds all my files with no issues. Previously my only solution was to use , I've been able to uninstall that now and use the standard Windows Start menu. I know to secure safety it is now not allowed anymore to open apps that were not downloaded from the mac app store.  But surely there is a workaround for this to open an app that you know is 'good' but just isn't in the app store. Preferably allowing only that app and not allowing all downloaded apps to be opened.    How do I open an app that is not downloaded from the app store in mountain lion? Find and replace text within a file using commands Where did object dimensions go in 2.8? launch app, capture stdout and stderr in c++ How do I launch an app and capture the output via stdout and maybe stderr?  I am writing an automated build system and I need to capture the output to analyze. I'd like to update the svn repo and grab the revision number so I can move the files in autobuild/revNumber/ if successful. I also would like to build using make and upload the compile text to my server for everyone to see the warnings and errors on a failed build.  I can't find the system() function, but I found the CreateProcess() function on MSDN. I am able to launch what I need but I have no idea how to capture the stderr and stdout.  I notice the process launches separately unless I set a breakpoint and keep my app exiting which it then will keep all the text in my app console window. I would also want to wait until all processes are finished and then scan the data it produced to do any additional operations I need. How do I do any of this?