Prove that the condition number of an invertible matrix must be at least 1.Please provide what matrices have condition number equal to 1?
Show that the condition number of an invertible matrix must be at least 1. What matrices have  condition number equal to 1.  If someone could help me with this and give an explanation that would be very helpful. I do not know where to start
How do I login to the Gamecenter on PewDiePie's Tuber Simulator, if you have not done it when they asked? 1.35 V RAM in a 1.5 V system - Will it fry or overclock? The general question is: When installing low voltage RAM in a board that outputs a higher voltage to the memory module, will this fry the RAM or will it be like overclocking it?  My specific case is: I have the Alienware m17xR3 laptop with a 2630QM Sandy Bridge board. Currently, I have the stock 1.5 V modules and when I check the overclocking options in my bios, the RAM voltage option ranges from 1.5 - 1.65 V. Is this simply because the bios recognizes that these are the values which my current RAM support and thus they will change when I install 1.35 V RAM or will I have to run the 1.35 V sticks at minimum 1.5 V?  If the case is the latter, would I fry my 1.35 V sticks? Or would they become automatically overclocked and get tighter timings with a higher voltage? Or both? Or neither? I'm a bit lost :p Show uncountable set of real numbers has a point of accumulation Show that every uncountable set of real numbers has a point of accumulation. WinDirStat shows 244GB unknown space on external drive I recently noticed that one of my external hard drive seems to be missing a lot of space. It was recommended that I try WinDirStat, as it could help identify how much space each file was taking up. This is the result:     As you can see, there is about 244.7GB "unknown" usage.  Doing a bit of research online, the most common suggestion was (a) Recycle Bin and (b) System Volume Information.  (a) As you can see, empty. To double check, I ran Disk Cleanup. It confirmed that it was empty. (Note that a new file appeared by the time I took this screenshot, but it's only 129 Bytes.)  (b) Harder to tell. However, according to various forums, the most common reason for System Volume Information to grow large is due to System Restore Files. I had a look, and it is definitely turned off for this drive, as seen here:     What else could be causing this issue? It is an enormous amount of storage to have gone missing! Can I connect copper wire to aluminum wire? Is there a way to export my artwork as PDF so that it has a transparent background? Something like exporting objects only... whenever I try to save my .ai as pdf, it always comes with a full white background. If I try to save as eps, I get a chunky white background (where it has white rectangles behind the artwork only where the artwork exists, so there are transparent chunks).  If I export as png, I get an image like what I'm looking for. Is there any way to do that in a vector format? On the Android app, could we have the ability to flag comments we've previously upvoted? This is a fairly regular need for me, and I ran into it again earlier: I flag comments as obsolete when they are, and fairly often, one of them will be a comment I've upvoted.  For an example of a typical case: a comment suggests a great improvement to a question, I upvote it, the author performs that improvement, the comment is now obsolete and (on my PC) I flag it as obsolete. The comments get cleaned up and the question moves on.  There's a request that's been around since 2011 for the site itself: . It's implemented by SOUP (as described ), but the Android app doesn't have a SOUP available to add this functionality to the app for me. How to find web hosting that meets my requirements? This is a "catch-all" question designed to serve as an answer for all questions about choosing web hosting.  Pro Webmasters no longer accepts new questions about how to choose hosting.  All future questions pertaining to finding web hosting should be closed as a duplicate of this question. For more information about this policy please see .    How to find web hosting that meets my requirements?  What we're looking for in answers to this question are the basics about web hosting:   What is web hosting? What is the difference between shared, VPS, and dedicated hosting? How does a content delivery network relate to web hosting? Anything else you feel is helpful in finding a web host.   What we do not want is:   Endorsements or recommendations for specific web hosts We do not want your experience or other subjective information (just the facts please) Creating checkbox parameter in Python script tool for ArcGIS Desktop? I am working on creating an ArcGIS tool from a Python script I am writing.  I am wondering if it is possible to have a checkbox parameter.    I want to have a parameter where the user selects a feature class, then from the feature class the user will choose the field for the upper most layer in their model, then I want the user to be able to choose what layers they want the script to run on with a checkbox structure derived from the upper most layer field.    Is this possible with python, and ArcGIS Desktop? Is there a way to exclude other particle systems from the effects of a Wind effect? I have a scene with a number of particle systems. I'd like to have a separate wind effect for my main scene and another for an extra: an emitter + wind-effect to blow leaves into my scene. I can't find any way to exclude, so here I am. At the very worst, I can just render the main scene and then render the wind effect and composite it, but I figured I'd check first. I use a dual monitor.  The colors appear entirely different on the new monitor than they do on my laptop.  When you are selecting colors etc, to be included in a website design, it totally freaks me out.  Is there no software solution that finds how the settings of one of the monitor is and puts that to the second one?  Otherwise what all settings do I need to change manually on the second monitor to make it appear as it does on the laptop?  Thanks in advance. How can I output a list of all installed packages with installation date and additional information? Why is jumping into water from high altitude fatal? If I jump from an airplane straight positioned upright into the ocean, why is it the same as jumping straight on the ground?  Water is a liquid as opposed to the ground, so I would expect that by plunging straight in the water, I would enter it aerodynamically and then be slowed in the water. I am trying to solve an integral in $k$-space where I want to calculate the ratio of the average energy of an arbitrary electronic band ($E(k)=k^n)$ to the square of average group velocity of electrons($v_g   = k^{n-1})$ approximately in the form of this expression given by $$L=\frac{\frac{\sum_{\mathbf{k}}k^{n}}{\sum_{\mathbf{k}}1}}{\left(\frac{\sum_{\mathbf{k}}k^{n-1}}{\sum_{\mathbf{k}}1}\right)^2}\;.$$  Now, I want to do this for $d$-dimensions, so I convert this sum to integral.  $$L=\frac{\dfrac{\int_{0}^{k_f}k^{n} d^d k}{\int_{0}^{k_f}1d^d k}}{\left(\dfrac{\int_{0}^{k_f}k^{n-1}d^d k}{\int_{0}^{k_f}1d^d k}\right)^2}$$ where $d^dk  = \dfrac{d \pi^{d/2}}{\Gamma(\frac{d}{2}+1)}k^{d-1}dk$ is the volume element in $d$-dimensional space.  I want to get a simple expression for $L$ and how it depends with $k_f,n$ and $d$. any physical insight into this integral could also be helpful. How to remove snap completely without losing the Chromium browser? How do you factorise $x^3z - x^3y - y^3z + yz^3 + xy^3 - xz^3$? I'm trying to factorise $$ x^3z - x^3y - y^3z + yz^3 + xy^3 - xz^3 $$ into four linear factors.  By plugging it into WolframAlpha I've learned that it's $$-(x-y)(x-z)(y-z)(x+y+z)$$  My question is: what are the steps involved in factorising the expression? Is there a method I don't know about that I'd have access to with my limited maths?  Really appreciate any help! Is there a non written rule to which person to use in the PhD thesis, 5 years of using "We" in the papers have brought me to the innate necessity to do it every time I describe something.  Recently, though, one of my lab-mates told me that I should use I, since it is your work, if the thesis were co-written, then it would be a different story.  Is there any standard in your universities, or do you have any preferred practice. How can I send the stdout of one process to multiple processes using (preferably unnamed) pipes in Unix (or Windows)? I'd like to redirect the stdout of process proc1 to two processes proc2 and proc3:           proc2 -&gt; stdout        /  proc1        \           proc3 -&gt; stdout   I tried   proc1 | (proc2 &amp; proc3)   but it doesn't seem to work, i.e.   echo 123 | (tr 1 a &amp; tr 1 b)   writes   b23   to stdout instead of    a23  b23 In iOS 8.4.1, if a caller who has 6 numbers, calls you and you see a missed call. Then, clicking the "i" symbol next to the missed call showed you all the 6 numbers of the caller and the number from which he called, was indicated with blue. This helped in knowing exactly what number he called me from and I could call back on the same number.  iOS 9.0.1 call log does not indicate the number the caller called from with blue (if the caller has more than one number). So, it becomes impossible to call the person back on the same number.  This was one very important feature that made iOS 8 very useful. Apple has taken away a very important feature. If $\gcd (a,b) = 1$, what can be said about $\gcd (a+b,a-b)$?