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I was asked this question in an interview.  Lets say we have a correlation matrix of the form \begin{bmatrix}1&amp;0.6&amp;0.8\\0.6&amp;1&amp;\gamma\\0.8&amp;\gamma&amp;1\end{bmatrix}  I was asked to find the value of gamma, given this correlation matrix. I thought I could do something with the eigenvalues, since they should be all greater than or equal to 0.(Matrix should be positive semidefinite) - but I don't think this approach will yield the answer. I am missing a trick.  Could you please provide a hint to solve for the same? Schengen refusal formulae can be difficult to understand sometimes.  Sometimes an applicant receives a refusal with:       Justification for the purpose and conditions of the intended stay was not reliable.     often accompanied by:       Your intention to leave the territory of the Member States before the expiry of the visa applied for could not be ascertained.   What is meant by this refusal reason?  What are they trying to say? Verification that $\lim_{x \to a}\frac{f(x)-f(a)}{x-a}$ and $\lim_{h\to 0}\frac{f(a+h) -f(a)}{h}$ are equivalent definitions of the derivative. I wanted to verify that for definition of the derivative it is true that:  $$ \lim_{x \to a}\frac{f(x)-f(a)}{x-a}= \lim_{h\to 0}\frac{f(a+h) -f(a)}{h}$$  If I denote $h=x-a$,  we can  let $x\to a$, this means that $h \to 0$. Also notice that $f(x)=f(a+h)$ $$ \lim_{x \to a}\frac{f(x)-f(a)}{x-a}=\lim_{h \to 0}\frac{f(a+h)-f(a)}{h}$$ As desired. Is the main idea here really just to use a variable substitution? I suppose there is some formal theorem I also use here that when $f(x) \to y$  we can let $g(f(x)) \to g(y)$ if the function $g$ is continuous. says:  Bash attempts to determine when it is being run with its standard input connected to a network connection, as when executed by the remote shell daemon, usually rshd, or the secure shell daemon sshd. If Bash determines it is being run in this fashion, it reads and executes commands from ~/.bashrc, if that file exists and is readable.  This Bash sources ~/.bashrc: ssh user@host :  But this Bash sources ~/.bash_profile: ssh user@host  I don't see a difference in these two commands according to the spec. Isn't stdin connected to a network connection in both cases? I'm planning to use ZFS on my system (HP ML370 G5, Smart Array P400, 8 SAS disk). I want ZFS to manage all disks individually, so it can utilize better scheduling (i.e. I want to use software RAID feature in ZFS).  The problem is, I can't find a way to disable RAID feature on the RAID controller. Right now, the controller aggregates all of the disks into one big RAID-5 volume. So ZFS can't see individual disk.  Is there any way to acomplish this setup? Optional Android notifications for reputation changes I would like to get a notification if my reputation count has changed. I think there is already some internal API for that. (I can see that changes in the menu bar in the top).  I'm sure that some people would not like that so that should be optional. Correct usage of will and would Consider the following sentence     It will/would rain tomorrow.   I understand "would" usually means something that is really improbable.  So "it would happen" means it might happen but it is very unlikely; while "it will happen" means it is going to happen  But what if I want to say      It will not happen?   Because the meaning of "it will not happen" represents something that is unlikely or, worse still, not going to happen, shouldn't it be more accurate to say "it would not happen"?  However, to contravene the aforesaid suggestion - if I am confident that the thing is not going to happen, should I use "will" to indicate the definite nature of my statement?  To further complicate the issue, what if I want to say     I think you will not be able to do it.    or      I think you would not be able to do it.    Which one is more accurate/correct,  given that "I think" already conveys a sense of "less than definite" and "will/would not be able to" conveys the same sense as "unlikely"? Which one should should I use? For some reason I have always used "towards", but I see some people saying "toward", like :     A great deal of his work in economic   theory has been directed toward   strengthening the foundations of our   understanding of central banking and   social insurance--indeed, one of my   most advanced macroeconomic classes   was nothing but a set of changes rung   upon a particular model that Peter   Diamond had advanced at...   Is there a difference between the two? When should they be used? When did Tom Riddle get his new face? Recently I asked about the  pertaining to Voldemorts new face. However I was corrected by ...     Well, I think the confusion comes with mixing movie canon with book canon. In Philosopher's Stone, here's what Harry sees when Quirrell unwraps his turban:           Harry would have screamed, but he couldn’t make a sound. Where there should have been a back to Quirrell’s head, there was a face, the most terrible face Harry had ever seen. It was chalk white with glaring red eyes and slits for nostrils, like a snake.          Philosopher's Stone - page 212 - UK - chapter 17, The Man With Two Faces      So it seems at some point between leaving school, and sticking his face to the back of Quirrel's head possessing Quirrel he got a new face some how.   How did he manage that? Is it some dark magic he applies? Is it from possessing snakes in Albania? strange character replacement on SO I added a comment to  but something strange is happening. The end code reads "); but SO decided to change that to ";);.    I did not add a ; in front of the ).  To further explain what's happening here, the following:  "http://example.com/." http://example.com/. "http://example.com." http://example.com. "http://example.com" http://example.com   renders as: Is it possible to install Windows from an external hard drive?  I have Windows XP installed on my laptop, and I want to remove it and install Windows 7.  My Windows 7 installation is in an .iso format on an external USB hard drive.  Is it possible to install it or will I need to put in a DVD before I start installing? Is there any way I can use  partitions on Windows&nbsp;7?  I have tried to install , but it doesn't seems to run on Windows&nbsp;7. After pacman update, pacsearch is no longer installed Midpoint-Convex and Continuous Implies Convex Given that $$f\left(\frac{x+y}{2}\right)\leqslant \frac{f(x)+f(y)}{2}~,$$ how can I show that $f$ is convex. Thanks.      Edit: I'm sorry for all the confusion. $f$ is assumed to be continuous on an interval $(a,b)$. How old is SpongeBob? How old is SpongeBob? I don't mean how old is the series, I mean what is SpongeBob's age if he were a real person. I ask because his age seems to be ambiguous in the show.   He has a full-time job He has his own house He is always referred to as a kid (especially in the movie) He acts childish and immature In one episode, he was pretending to be an adult/grown-up I lock my computer a lot, and was wondering if there was a way to get the lock screen when I hit Ctrl + Alt + L. Right now when I use that key combination it turns the screen black, and I have to hit a key or click to bring up the screen where it shows the option to enter your password or switch users, as well as displaying the desktop background behind it.   Is there anyway to avoid having to hit that extra key, to bring up the screen I want? And is there anyway to keep it that way? It's really a matter of personal preference, and I don't see any reason why not to have it stay that way as my monitor eventually is turned off and/or my computer suspended. iPhone, reproduce the magnifier effect How to use exclamation marks in Minecraft commands? Why my tweet is not appearing on the timeline of the person I am following? I have tried tweeting someone I follow couple of times.  My tweets appear on my profile but when I look at the other person's timeline, my tweet is not there. I am following him but he is not following me. Unable to install any updates through update manager/apt-get upgrade