I'm doing principal component analysis on my dataset and my professor told me that I should normalize the data before doing the analysis. Why?   What would happen If I did PCA without normalization?  Why do we normalize data in general?  Could someone give clear and intuitive example which would demonstrate the consequences of not normalizing the data before analysis?
What are the main differences between performing principal component analysis (PCA) on the correlation matrix and on the covariance matrix? Do they give the same results?
How do I remove Ubuntu's password requirement? Accessing derived class property members from base class object in CSharp I've been working with the Fermat numbers recently, but this problem has really tripped me up. If the Fermat theorem is set as $f_a=2^{2^a}+1$, then how can we say that for an integer $b&lt;a$, the $\gcd(f_b,f_a)=1$? I know this issue has been addressed before with different software, but how do I do it with Shapely?  I have a polygon with a very small gap on the interior of the shape:    Here is a close up:    The polygon is valid so I can't use the buffer trick, and simplifying the polygon also doesn't work. Is it possible to install MySQL 5.5 or 5.6 on Ubuntu 16.04? I recently upgraded to Ubuntu 16.04. Unfortunately I need to work MySQL 5.5 or 5.6. I tried many solutions to have MySQL 5.5 or 5.6 run on Ubuntu 16.04 like this  . But none of them is working. Ubuntu detect the unmet dependencies but says "but it is not going to be installed" for 5.5 or says Package 'mysql-server-5.6' has no installation candidate...  Is it not possible to force an earlier version of MySQL on Ubuntu? Why is that? Can jQuery .load append instead of replace? Reset post score to 0 on migration I suggest that when a post is migrated from one site to another, that the question vote score get reset to zero (or perhaps only a negative vote score is reset to zero). Often people will downvote a question when the only thing that's "wrong" with it is that it's posted on the incorrect site. After migration, those downvotes hang around as a negative score and may unfairly bias the treatment of the question. Why is the derivative of a vector orthogonal to the vector itself? $R(t) \cdot R'(t) = 0$, which is what every source I can find tells me. Even though I understand the proof I don't understand the underlying concept. If $R(t)\cdot R'(t) = 0$, then $R'(t)$ is orthogonal to $R(t)$, right?   But you use the same derivative to find the tangent of a curve. Then somehow if you differentiate the tangent itself, you get the normal to the curve.  I really can't wrap my head around this. Could someone help me understand? "Require Installation Of Untrusted Packages" while upgrading with the update manager It didn't fixed the error. So, how do I fix my GUI update?  For every software I have to install it from command line because I got same error when install software from Ubuntu Software Center. Getting the name of the currently executing method Remmina remoteapp over RDP I was wondering how to use remmina to open applications on a Windows machine over rdp using remoteapp (or seamless or whatever it's actually called).  I've already used Kim Knight's  to set up remoteapp on a Windows 7 machine and I can connect and run remote apps fine from another windows box.  Allegedly FreeRDP (which Remmina uses for its RDP Plugin) has support for remoteapp. I'm not sure how to make use of it though. I can't find any examples of people actually doing this online but there is a , from which I can infer that there is some way to run remote apps.   I've tried many combinations of settings for Client, Startup Program and Startup Path in the Advanced tab when configuring an RDP connection in Remmina, but I can't make it work. I can connect to Windows boxes with RDP just fine, just not running a remoteapp. Hi im new to Blender and i want to know when im in edit mode if i can copy or cut a selections of polygons faces and paste to another mesh.  Thanks in advance for any help Structure of ideals in the product of two rings Difference Boolean modifier. How do I get it to work with my mesh? I want to make a screw head, but I can't get the cross in the screw head; the Boolean modifier doesn't work.  Link: Is there ever a right time to upgrade to full frame camera body? Context  I've been shooting with an a6000 (APS_C mirrorless) and I plan to move on up to full frame, preferably mirrorless as well. I'm debating on when to upgrade, and probably don't plan to buy until next year.  I know I'll need to buy new full frame lens.  Question  Is there a "right" time to buy camera bodies, both mirrorless in my case as well as DSLRs? (I've seen the a7rII and like it but there might also be an a9 looming.) I feel that this is like smartphones in which the best time to buy is now as you might always be waiting until the next upgrade.   Related, are full frame bodies discounted during the holiday season or is that limited only to entry level bodies and older full frame bodies?  Related Will it be possible to update Windows XP after April 2014? Closure of a certain subset in a compact topological group If I need to use Blender within a colour-accurate workflow, what do I have to do to set that up (including hardware calibration, etc)? When we canonically quantize the scalar field in QFT, we use a Lorentz invariant integration measure given by $$\widetilde{dk} \equiv \frac{d^3k}{(2\pi)^3 2\omega(\textbf{k})}.$$  How can I show that it is Lorentz invariant? Can I visit Chicago during a 5.5 hour layover in O'Hare?