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Inverse of a diagonal matrix plus a constant I am looking for an efficient solution for inverting a matrix of the following form:  $$D+aP$$   where $D$ is a (full-rank) diagonal matrix, $a$ is a constant, and $P$ is an all-ones matrix.   gives a solution to the special case where all diagonal entries of $D$ are the same.  The  formula is also capable of providing a solution to this problem by setting appropriate $u$ and $v$, but it loses efficiency ($O(n^3)$ time complexity to compute) at high dimension. I am hoping to get a result in the same form so the space and time complexity are both $O(n)$. In C# check that filename is *possibly* valid (not that it exists) Is there a method in the System.IO namespace that checks the validity of a filename?  For example, C:\foo\bar would validate and :"~-* would not  Or a little trickier, X:\foo\bar would validate is there is an X: drive on the system, but wouldn't otherwise.  I suppose I could write such a method myself, but I'm more interested in a built-in one. Why is the present perfect used in headlines? In news reports, we often read or hear events introduced with the present perfect, and then the past simple like this:     The film star Jim Cooper has died of cancer. He was 68 and lived in Texas.   What's wrong if we use both first and second sentence in past simple?     The film star Jim Cooper died of cancer. He was 68 and lived in Texas. Video produced from images only plays in VLC but no other players Is there a better way to do optional function parameters in JavaScript? vectorized array creation from a list of start/end indices Show that $xy=0$ is a variety but not a manifold multi-layer board copper pour I have a 6-layer board where the internal 4 planes are +15,GND,VCC,-15.  I was wondering if there was any advantage to doing a copper pour on the top and bottom layers?  I would probably leave them floating as I don't want to use micro-vias to say tie it to GND?    Is this actually a bad idea?  I.e. floating copper=antenna.  Would it be just as acceptable to have 4 layer board with the top layer having copper pour to VCC and the bottom having a pour to GND and keep the two internals as +-15?  Note that this is for a fairly low speed circuit which has some analog and digital parts. Is there a keyboard command for 'show desktop'? Like Windows, I want to hit Super+D to jump to the desktop or minimize all windows. I don't see command like that in Keyboard Shortcuts. Any idea? How can I skip every even item in the enumerate environment without having to continually type \setcounter{enumi}{5}? I am still learning to program macros, so I spologize if this is a ridiculously easy question.   Just to be clear, I would like something like   1. *Something.* 3. *Somthing else.* 5. *A third something.*  ...As opposed to   1. Something.  2. A second something.  3. A tertiary Something. In bash, how can I convert a Unicode Codepoint [0-9A-F] into a printable character? I have a list of Unicode codepoints, but I don't know of a "simple" way to convert these hex values into the actual characters they represent...    I've heard that zsh has echo -e '\u0965', but I use bash 4.1.  Is there something as simple as the zsh method, for bash? User suggested great corrective edit to my answer, but the edit was rejected. What can I do to approve it? Books for general relativity What are some good books for learning general relativity? Can I partition a HDD for playing Xbox 360 games? I am planning to buy an xbox 360 console. my budget permits me acess to only the 4 GB one which needs extra space for many games' install. I have an external HDD of size 40GB. My question is can I divide it into partitions such thet I can use one for gaming on xbox and the other for data storage. Plot an elliptic curve in Latex I have created multiple objects, while testing I applied a drop shadow style on one object and its looking very good. Now I want to apply the same style to all other objects (around 20). Is there any way like global color to create a style once and apply to other objects with single click automatically?  Or I have to apply that drop shadow effect on each object one by one manually? Assigning strings to arrays of characters I am a little surprised by the following.  Example 1:  char s[100] = "abcd"; // declare and initialize - WORKS   Example 2:  char s[100]; // declare s = "hello"; // initalize - DOESN'T WORK ('lvalue required' error)   I'm wondering why the second approach doesn't work. It seems natural that it should (it works with other data types)? Could someone explain me the logic behind this? What are the pros and cons of having a separate home partition? Unable to stylize raster data as pseudocolor render type on MAC OSX In a raster layer's Style Properties, I can choose pseudocolor render type, and choose a color ramp and classify the raster.      However, when I click the 'Apply' button, or click 'OK', the visualization of the raster never changes.  I was able to output a 'colorized' version of the same raster using GRASS plugin.  I also reinstalled QGIS 2.8, and was able to adjust and see a raster stylings using the steps I outlined above.  So, can anyone confirm this as an issue, or confirm that there's a mistake somewhere in my process?  I should note that I'm on a Mac, 10.10.4, and I'm using the QGIS provided by , 2.10.1-1 .  Update 1: Here's a screenshot of the rest of my settings.      I have Grayscale set to off in the Style setting.  Also, I don't believe grayscale/color-blind Preview is available on the Mac version of QGIS.  They're does't appear to be the option where it , in the Menu Bar under View / Preview / Photocopy (grayscale) etc.  Either way-- I added a shapefile to show color.  Update 2: I've experimented with setting color interpolation to discrete, linear, and exact, but still am not able stylize using Singleband pseudocolor.  I've also confirmed that the 'Render' box on the the main map view is checked.  Also, I am able to adjust Color Rendering settings, like Hue, Blending Mode, etc., and see the results when clicking 'Apply' or 'OK'.  Update 3: As other Mac users are confirming this, I think it may be a bug. I've created a bug report at the official . I'm on the hunt for a great sounding, non-in-ear set of headphones with working mic, play/pause, and volume buttons.  I have Bang &amp; Olufsen's , which are among the best sounding headphones I've ever used. And all three button work perfectly in my MacBook Air and iPhone.  Obviously they don't work perfectly in my Nexus 4, since Android devices uses a different way of reading volume up/down buttons.  So, my question is rather simple, does anyone know how to make them work with Android, or alternatively any equally good headphones to the EarSet 3i's that work on Android? And to make it extra challenging, no in-ear ones please, cause I can't stand them :(  Or maybe anyone knows of some kind of adapter cable that can be used between an Android phone and iPhone compatible headphones to translate the volume button signals so the Android device understands them?