What is the necessary and sufficient condition for the matrix $A = I − 2xx^T $to be orthogonal?
Necessary and sufficient condition for the matrix $A = I - 2 x x^t$ to be orthogonal
A map is continuous if and only if for every set, the image of closure is contained in the closure of image Dissolve (merge) polygons QGIS based on attribute values only when are adjacent 9 rows is just way too small by default. Is this a text-editor for ants? How should a user's death be handled? What's the best way to extend the User model (bundled with Django's authentication app) with custom fields? I would also possibly like to use the email as the username (for authentication purposes).  I've already seen a   to do it, but can't decide on which one is the best. I used exposure compensation when I take my shots and adjust it whenever it needs adjustments. Most of the time I shoot using Manual mode.  My problem is, when I'm out on a sunny day I can't judge whether my shot is overexposed or underexposed because the sun is too bright. Sometimes when I checked my viewfinder the image looks perfectly exposed to my eyes, but when I check it on my computer when I get home the images looks underexposed or overexposed. I tried to judge my shot's exposure using histogram, but still having a hard time. The only thing I understand about the histogram is that, the right side is the highlights and the left side is the shadow.  How do you judge whether the shot is overexposed or underexposed when you are out on a sunny day? How can I add a new user as sudoer using the command line? After I add a user using adduser, I can't see it via System > Administration > Users and Groups unless I log out and then log in again. Is that normal?  Also, can I set a newly added user as a sudoer or do I have to change that only after adding it? How can I do that via the shell?  Finally, can I delete the original user that was created upon initial installation of Ubuntu, or is this user somehow 'special'? pgfplots legend style for plots with error bands Fastest method to determine my PC's IP address (Windows) This may seem trivial but I'm looking for the quickest method to determine my PC's IP address within my network.   This changes regularly as I connect from one network to the next via DHCP The connection changes from wired to wireless Windows 7 PC (although ideally the perfect solution would work on all versions of Windows) Various adapters installed (e.g. VMWare, Tunnels, etc.)   I need to know this as I often run a local web server where I need to access files over the local network... and since it changes regularly I want the fastest method to retrieve the address.  My current flow is:   WindowsKey + R to open the Run dialog "cmd" + Enter to open a command prompt "ipconfig" + Enter to get the diagnostics info Scroll to or resize the window so that I can see the line in my Ethernet adapter Local Area Connection for my ipv4 Address Remember it to type elsewhere... or  Right click > select Mark > highlight the address > press Enter to copy it to the clipboard   This wasn't so bad with Windows XP when I had no additional adapters, tunnels, wireless connections etc. but the amount of data returned with this command makes it hard to pluck out.  Surely there must be a better, faster way! (bonus points if adding it to the clipboard is easily accomplished) Down vote changed to up vote caused reputation meter to pass daily maximum I just experienced a minor visual bug.  I had an answer that earned 2 down votes and 22+ upvotes, earning me the daily maximum of +200. Upon making some edits to the answer at the behest of the comments, one of the users who down voted changed their vote. Now my reputation meter shows that I gained +202 for the day.    This correctly did NOT affect my reputation, as I still only gained 200, so it is merely a minor display bug.  This appears in the achievements drop down and my reputation tab on my profile. How to speed my too-slow ssh login? Running ssh user@hostname takes ~30s. Here's the scenario:   this is a VM on the local LAN Windows and Mac machines get instant login am using Debian and I could reproduce with an Ubuntu machine someone using Ubuntu says that logging into my machine (local LAN) is also instant using hostname IP address takes about half as much time (~15s)   [update]  Using ssh -vvv user@hostname, here's where it waits the most:  debug3: authmethod_lookup gssapi-with-mic debug3: remaining preferred: publickey,keyboard-interactive,password debug3: authmethod_is_enabled gssapi-with-mic debug1: Next authentication method: gssapi-with-mic   And then it waits a bit here:  debug1: Unspecified GSS failure.  Minor code may provide more information Credentials cache file '/tmp/krb5cc_1000' not found  debug1: Unspecified GSS failure.  Minor code may provide more information Credentials cache file '/tmp/krb5cc_1000' not found list transparency across non consecutive slides This has been puzzling me for a few days now, and I asked a graphic designer I knew before trying here and haven't been able to solve it yet. It's quite weird so please bear with me for a bit.  I am using Adobe Illustrator to create a logo, and I have something that can potentially work. I have used only the pen tool with strokes (no fill), but the issue is, when I view the logo at 100%, it looks pixellated! I know vectors should not even be able to appear pixellated, but they are. Here is the screenshot from AI, without exporting to anything:     That was just done using the snipping tool within Windows, and it's at 100% zoom.  I have anti-aliasing turned on from Edit > Preferences > General, and the document resolution is at 300 ppi (I get the same result with 72 ppi).   Could anyone help me with this?   If relevant: Using CS6, and have a 24 inch Dell U2412M at 1920x1200 resolution. I do have a 21.6" Samsung at 1680x1050 and I get the same result there as well. Let me know if you need any other settings, or if you would like the file, I'd be happy to provide it to be able to solve this problem. In a table, how can I draw a horizontal line that goes only through some of the cells? I mean a line like the one in the Foo and in the Bar area of this table:  +----+-----+ |Foo |1 |2 | |    |1 |2 | |    +--+--+ |    |1 |2 | |    |1 |2 | +----+-----+ |Bar |1 |2 | |    |1 |2 | |    +--+--+ |    |1 |2 | |    |1 |2 | +----+--+--+ Levels or First Differences, VECM or VAR for Ultimate Impulse Response Functions? My final goal is to generate Impulse Response Functions in R.  I have variables that are non stationary when I set k = 5 in a Unit Root test, and they are cointegrated which to my understanding prompts the use of the VECM, from which the Vec2Var argument is used to then generate IRFs. However, my response functions from this methodology do not decay over time and mostly do not revert to the zero line.  Furthermore, I noticed that when I input first differenced variables into the VECM as opposed to level data above, response function do revert to the zero line. Therefore my first question is: 1) is it appropriate to use differenced variables in a VECM model?  Secondly, as an alternative I am considering restricting the number of lags used in the Unit Root tests so that the variables are not all non-stationary; in this case 2) would the use of VECM be void and the VAR with first differences be a more appropriate model? Again, using differenced data is giving me better response functions that revert to zero in the long run. However, 3) is it ok to use the VAR for stationary/non-stationary data in levels where these variables are still cointegrated?  Also, I am using growth rate variables, 4) should I still long transform all variables and use logs in all tests?  Thank you for the help! I want to color sketches in Photoshop, but when I prepared the sketch (using Levels, Hue, and other modifications) to turn it into workable line art, some details were missing. I think it depends on how you draw your sketch.  What are important steps for drawing a sketch (with pen or pencil) that is to be colored in Photoshop? A step-by-step instruction would be appreciated.  For instance, here it is the sketch    This is after my preparations in Photoshop Is it possible to pagebreak aligned equations? The report I'm writting features a lot of long, multiple lines equations. To reduce visual polution I've been using an aligned environment nested inside equation. This way (unlike just using an align environment) I get only a single label for all the lines.  The problem is that so many long equations often need to be broken into two pages, otherwise I get lots of blank vertical space in the document. However the aligned environment does not allow the \displaybreak command.  Is there an alternative way to achieve a pagebreak inside an aligned equation?  Here's a sample ofthe equations I'm using  \begin{equation}     \begin{aligned}     ...\\     ...\\  %I need to pagebreak here     ...\\ \end{aligned}\end{equation} Issue with 'StringVar' in Python Program Replace all occurrence of character except first one Is there some way to PUSH data from web server to browser? Of course I am aware of Ajax, but the problem with Ajax is that the browser should poll the server frequently to find whether there is new data. This increases server load.  Is there any better method (even using Ajax) other than polling the server frequently?