Let M be mxn matrix then SVD of M will be UXW^* (sorry for X, assume summation). Then how does it generalizes eigen decomposition ? Since eigen decomposition is possible for nxn matrix and that are non-symmetric.
Principal component analysis (PCA) is usually explained via an eigen-decomposition of the covariance matrix. However, it can also be performed via singular value decomposition (SVD) of the data matrix $\mathbf X$. How does it work? What is the connection between these two approaches? What is the relationship between SVD and PCA?  Or in other words, how to use SVD of the data matrix to perform dimensionality reduction?
What is this element on the far right of schematic described as "270 OHM"? Is this some kind of inductor? What is its purpose in this device (this is a reference design of dc-dc power supply of sim900 taken from its datasheet) and what would be an exemplary part number? Why do modern mountain bike forks no longer use boots on fork stanchions? Older mountain bikes used to have them on the forks, and lefty and headshocks still do. Why have these fallen out of fashion and would putting aftermarket fork boots on your stanchions be productive or not? Earlier, I voted to close  as off-topic.  The question has since been closed.  There is an , but it didn't show up in the list when I selected "off-topic".  The options were:   Meta Stack Overflow Server Fault Super User Webmasters Programmers   Questions:   Should Wordpress appear in this list? Are there any other sites that should appear in the list?   Should all non-beta sites appear in that list by default? Origin of electric charge Baryons have charges that are the result of a polynomial calculation of their building blocks (quarks)'s fractional charges. But what gives these quarks electric charges? What interactions do they have with photons? And what about leptons, like muons and electrons? How do they get their -1 charge? And then, how do positrons and anti-muons get +1 charge? Same goes for quarks: how does up-antiquarks get -2/3 charge? Or I may want to formulate my question this way:  How does any elementary particle interact with the EM-Force to get an electric charge? Create a new cmd.exe window from within another cmd.exe prompt Set the default permission when creating a file Why can't a class extend its own nested class in C#? For example:  public class A : A.B {     public class B { } }   Which generates this error from the compiler:     Circular base class dependency   involving 'A' and 'A.B'   I always figured a nested class behaved just like a regular class except with special rules concerning accessing the outer class's private members, but I guess there's some implicit inheritance occurring between the two classes? How do I restore a Places folder I accidentally deleted in Nautilus? How to count number of bases and subspaces of a given dimension in a vector space over a finite field? Let $V_{n}(F)$ be a vector space over the field $F=\mathbb Z_{p}$ with $\dim V_{n} = n$, i.e., the cardinality of $V_{n}(\mathbb Z_{p}) = p^{n}$. What is a general criterion to find the number of bases in such a vector space? For example, find the number of bases in $ V_{2}(\mathbb Z_{3})$. Further, how can we find the number of subspaces of dimension, say, $r$?   I need a justification with proof. I have a formula, but I am unable to understand the basic idea behind that formula. Using jQuery, how do I change the elements html value? (div) Using a ajax request I want to change content of my div.  &lt;div id="d1"&gt;202&lt;/div&gt;   So I want to change the content to a different number.  $('d1').InnerText???   Also, say I wanted to increment the number, how could I do that? Do I have to convert to int? How to check if a column exists in a SQL Server table? I need to add a specific column if it does not exist. I have something like the following, but it always returns false:  IF EXISTS(SELECT *           FROM   INFORMATION_SCHEMA.COLUMNS           WHERE  TABLE_NAME = 'myTableName'                  AND COLUMN_NAME = 'myColumnName')    How can I check if a column exists in a table of the SQL Server database? Pdf bookmark error in beamer Hi. I've compiled a Persian language beamer file by both luapersian and persian babel package using LuaLaTex, and in both I've the same problem in pdf bookmark as shown in the figure (some strange characters are shown instead of correct characters). Programmatically Create X509 Certificate using OpenSSL I have a C/C++ application and I need to create a X509 pem certificate containing both a public and private key.  The certificate can be self signed, or unsigned, doesn't matter.  I want to do this inside an app, not from command line.  What OpenSSL functions will do this for me?  Any sample code is a bonus! Is "Logan" the last movie with Hugh Jackman as Wolverine? has played the role of Wolverine as a major character in various X-Men films since 2000 and contributed highly to the brand of the X-Men movie series. But is he playing the Wolverine character for the last time in Logan?  I am getting to know from my friends that  is the last movie in which he is playing Wolverine and they all say that this is his last contracted film.  Are these rumors true? Is there any official information that confirms that this is Hugh Jackman's last movie as Wolverine? How can I SSH with a remote server so I can browse files and edit them? I have a username and password to use. I installed few environments that I wanted to try out on Ubuntu 12.04, but none of them worked at all. It could be that I installed them all at the same time, meaning the OS didn't get a chance to work everything out, but either way, they didn't work. I would now like to remove them.   The one's that I installed are Xubuntu/Xfce, Lubuntu/LXDE, Kubuntu/KDE, Fluxbox, OpenBox, cinnamon, and MATE. I installed them. Everything seemed to have been working properly until I actually tried to use the shells and nothing loaded at all. Except for Fluxbox, I think that one worked. I want to know of any way to repair or perhaps just remove the packages entirely. I might have already removed them because I did the apt-get remove command on all of them, but they were still in the list on the login screen. I want to merge two shape files in which one is of point geometry type and other is polygon type in order to get a single layer containing both points and polygon in a single map. Intuition for $\,c\mid a,b \iff c\mid \gcd(a,b)$ Why do the Localization of a Ring This question may be a bit vague, but neverthless, i would like to see an answer. Wikipedia tells me that:   In abstract algebra, localization is a systematic method of adding multiplicative inverses to a ring.   It is clear that for integral domains, we have the Field of Fractions, and we work on it. It's obvious that a Field has multiplicative inverses. Now if we consider any arbitrary ring $R$, by the definition of localization, it means that we are adding multiplicative inverses to $R$ thereby wanting $R$ to be a division ring or a field. My question, why is it so important to look at this concept of Localization. Or how would the theory look like if we never had the concept of Localization. What is the name of the default font in math mode? I draw figures in Inkscape. When I label elements within the figures with variable names that I have used in the underlying TeX document, I would like them to look exactly the same as in the document. (e.g. l does not look the same as $l$)  What is the name of the math mode font so I can select it correctly in the Inkscape font list?  If the exact font should not be available, what is a similar looking font that is present on most systems?