Is normality test required for original data prior to the principal component analysis?
Applying PCA to data that fail a normality test
Why isn't the eigenclass equivalent to self.class, when it looks so similar? Meaning of U suffix How to share data between forms? In Einstein's General Relativity, do the space-time dimensions curve? In Einstein's General Relativity, do the space-time dimensions curve according to the positions of stars, planets, and masses? For which $n$ is the sum: $$\sum_{k=0}^{n}10^k$$ a prime number? Are they finite? As we all know, immediate actions are just like swift actions, but can be performed outside of one's turn.     However, unlike a swift action, an immediate action can be performed at any time - even if it's not your turn.   However, it is still unclear if one can use an immediate action during someone else's action.  For example:  A monster swings at a conjurer.    Can conjurer abrupt jaunt outside monster's reach right after the attack was rolled, thus wasting an attack?  What about right after the damage was rolled, but not yet applied?  What about casting celerity and baleful transposition on yourself and monster's ally so the monster would hit his ally, given high enough attack roll?   Let's complicate a bit with a complex, full-round action on a monster's side.    Can one use immediate action in between attacks in full attack? What about after movement part of a charge? Down arrow button for choosing the desired site I want to use the GameJolt API, how do I protect my private key which is in my game? GameJolt is a gaming platform/website that offers API access with features like achievements tracking for users, etc. I can use the API no problem on my tests but what I'm concerned about is the private key that is issued to my game. How do I ensure that it's protected from people that want to decompile my game? Once  they get the API private key, they will be able to do anything with it. We have 10 PC with some version of Ubuntu and only remote access. While doing some upgrades to custom software I did not notice that the line endings in some scripts were Windows version (CR+LF) and not the Unix version (LF). So now when I want to launch the script it gives an error:   bash: /usr/local/bin/portsee: /usr/bin/python^M: bad interpreter: No such file or directory   Is there a way to change all line endings in a script from terminal. The thing is that I can not install any new software to this group of PC-s. Here is my proof, I would appreciate it if someone could critique it for me:  To prove this statement true, we must proof that the two conditional statements ("If $\mathcal{P}(A)⊆ \mathcal{P}(B)$, then $A⊆B$," and, If $A⊆B$, then $\mathcal{P}(A)⊆ \mathcal{P}(B)$) are true.    Contrapositive of the first statement: If $A \nsubseteq B$, then $\mathcal{P}(A) \nsubseteq \mathcal{P}(B)$  If $A \nsubseteq B$, then there must be some element in $A$, call it $x$, that is not in $B$: $x \in A$, and $x \notin B$. Since $x \in A$, then $\{x\} \in \mathcal{P}(A)$; moreover, since $x \notin B$, then $\{x\} \notin \mathcal{P}(B)$, which proves that, if $A \nsubseteq B$, then $\mathcal{P}(A) \nsubseteq \mathcal{P}(B)$. By proving the contrapositive true, the original proposition must be true.    To prove the second statement true, I would implement nearly the same argument, so that isn't necessary to write. So, does this proof seem correct? Also, was the contrapositive necessary? Or is there another way to prove the initial statement? I  to the question "" which was specific to the question asked.  Another user engaged positively with my answer, as there was a small conversation thread.  That person then  and made what I would say are minor modifications (the comments I left in my original code that pertained to the specific case are still in the places where he made edits to be more specific).  The answer does acknowledge that it is a general case of my specific code.  Ignoring the fact that I'm involved in it, what should one do when seeing this situation?  The only thing I can think of, and I'm not sure that it's necessarily the right solution, is to flag the answer for moderator attention.  Other possible actions, which I believe are wrong, are:   Editing the answer; that would change its intent Voting the answer down; it's a technically correct answer   One could leave a comment, but that can lead to confrontation and escalation (depending on the parties involved) which would be counterproductive.  The only thing I've done, which is not really related, is edit the answer to hyperlink the already existing attribution (but I do this as a regular edit for any answer which explicitly references another).  What's the best approach here, if any? How do the Planets and Sun get their initial rotation? Why do Venus and Mercury rotate so slowly compared to other planets?  Why does Venus rotate in a different direction to Mercury, Earth and Mars? What is the "maybe" caller id suggestion in the call log based on? I got a call from a phone number that is not stored in my address book, and in the call log, under the number, a name was suggested: "Maybe: X" (where X is the guessed name).  Where is this guess coming from? How to visualize the gradient as a one-form? I am reading Sean Carrol's book on General Relativity, and I just finished reading the proof that the gradient is a covariant vector or a one-form, but I am having a difficult time visualizing this. I usually visualize gradients as vector fields while I visualize one-forms with level sets. How to visualize the gradient as a one-form? Remove Archives in category title How I can remove word "Archives" in head title in category page? I'm using the Twenty Twelve theme and WordPress 4.   &lt;head&gt; &lt;title&gt;"name of category" Archives  | "name of sites"&lt;/title&gt; &lt;/head&gt; Putting a piece of code in between two html tags in Solaris On a solaris HTML file, how do I insert between an html tag and head tag? through bash scripting.  I have an html tag that looks like this:  &lt;html xmlns="http://www.w3.org/1999/xhtml" xmlns:arf="http://scap.nist....-format/1.1" lang="en"&gt;   I want to insert a script written in text file, inside this 'SOLARIS' run HTML file, AFTER the long &lt;html....&gt; tag and BEFORE &lt;head&gt; tag, meaning BETWEEN the two tags, How do I do that?  I want to test using the bash commands to do it for one file at a time as well as multiple file in a folder directory. Will I have to use the folder path in my BASH code? Will I have to use FOR loop or interation in my BASH code? What would be the right code. Note: it is SOLARIS run html file not LINUX one. The name of my HTML file is report.usc20.html.  These are the lines of script that I want to use that are in my backbutton_and_scroller_script.txt file:  &lt;div id="button"&gt;&lt;a href="http://.....index.php"&gt;Back To The Hardening Page&lt;/a&gt;&lt;/div&gt; &lt;script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.3/jquery.min.js"&gt;&lt;/script&gt; &lt;script type="text/javascript" src="http://arrow.scrolltotop.com/arrow78.js"&gt;&lt;/script&gt; &lt;noscript&gt;Not seeing a &lt;a href="http://www.scrolltotop.com/"&gt;Scroll to Top Button&lt;/a&gt;? Go to our FAQ page for more info.&lt;/noscript&gt; Windows 7 stuck on CLASSPNP.SYS I'm running Win 7 x86 on a Lenovo Thinkpad Z61m in dual boot mode with Win XP, both OSes are running on separate partitions. I have a faulty battery and if left unplugged my laptop shuts usually down within 10 minutes. Last night, it shut down due to this, but after plugging in AC power and starting back up I'm stuck at the "Starting Windows" screen, I'm unable to boot into safe mode or into recovery mode(XP boots fine).  I believe I had installed some Win 7 updates the same/previous day. From one of the boot options I was able to see that Windows 7 is getting stuck on CLASSPNP.SYS  How can I go about fixing this?  I do have a complete Win 7 Restore CD that I created after setting up my machine, I'm unable to boot into this either.  Please help! prove that $\mathbb{Q}^n$is dense subset of $\mathbb{R^n}$ Prove that $\mathbb{Q}^n$is dense subset of $\mathbb{R^n}$ using the fact that $\mathbb{Q}$ is dense subset  of $\mathbb{R}$  I know that $\mathbb{Q}$ is dense subset  of $\mathbb{R}$ That is, between any two real numbers, there exists a rational number  then how to prove that $\mathbb{Q}^n$is dense subset of $\mathbb{R^n}$ Consistency of an order statistic in exponential distribution Our son is about to turn 3 months but he is yet to sleep on his own (as in we put him to sleep, put him down on the crib then he sleeps for few hours). He only sleeps when he is carried during the day, the moment we put him down he wakes up crying. At night, he sleeps with us on the bed where he is right next to his mommy. We blame ourselves for letting this happen but now my wife can't do anything during the day but carry him.  What can we do to break him out of this habit? Any pointers would be great appreciated.