I have already posted my problem in stackoverflow, I am not sure if this might be problematic, and I am not sure, if the post is shown in both communities. If so I will delete.  I am trying to apply principal component analysis, to reduce the dimensions of my data. 200x146 , 200 observations(samples) with 146 features(dimensions), each observation can belong to one of three classes. What I am trying to do is to visualize the data, to see how the class centroids move after adding new samples to my data. Since it’s impossible to plot such high dimensional data, I am looking for a dimension that would represent my data in almost separate classclusters.  I know that PCA, calculates the eigenvalues of the eigenvectors, while the eigenvalues represent the variance. The higher the variance the more the data is spread out and better to visualize. The eigenvector with the highest eigenvalue is the principal component, an axis orthogonal to this component is then found by the PCA. (Did I understand the basic idea of PCA correctly?)  However I don’t understand, what information I do get when I use the matlab function pca() I get the coefficient, but what do they tell me and how to I proceed afterward?
In today's pattern recognition class my professor talked about PCA, eigenvectors and eigenvalues.   I understood the mathematics of it. If I'm asked to find eigenvalues etc. I'll do it correctly like a machine. But I didn't understand it. I didn't get the purpose of it. I didn't get the feel of it.        I strongly believe in the following quote:     You do not really understand something unless you can explain it to your grandmother. -- Albert Einstein   Well, I can't explain these concepts to a layman or grandma.   Why PCA, eigenvectors &amp; eigenvalues? What was the need for these concepts? How would you explain these to a layman?
Splitting pieces of a mesh into a new object Reattach to lost X11 session I'm using X11 forwarding over ssh to run Linux apps on my Windows box, and when the network drops it loses everything that was running. Is there anything similar to screen for X11? Unable to install any updates through update manager/apt-get upgrade How can I make a view that seems like orthographic, but not exactly? For the start, I thought was orthographic, but when I used the orthographic camera, it didn't match up. Client say they want a so-called &quot;industry schematic&quot;, talking about a 135 degree look.  I found a trick to do this, which is using lattice. I align the lattice with the cube, and move the upper four points a little bit along the axis showing on the following image. But I want to achieve this by just using the camera. In the book I'm study is written:     A normal subgroup of a group need not be characteristic.   And as an exercise I'm supposed to find an example, it also said that is pretty hard to find one. After trying for two days I wasn't able to find one example.   So, I'm asking for an example of a group $G$ with a normal subgroup $H$ that is not a characteristic of $G$.  I will add some context because maybe it will clarify why the book said it is difficult to find an example: the main problem with the exercise is that until it the book had only covered Group Definition, Subgroups, Lagrange's Theorem and Homomorphisms. So I'm supposed to find a example with such lack of advanced tools. Apparently I cannot count. I think there are three files in /media  $ tree /media /media ├── foo ├── onex └── zanna 3 directories, 0 files   However, ls -l finds 12.  $ ls -l /media total 12 drwxr-xr-x  2 root root 4096 Jul 31 20:57 foo drwxrwxr-x  2 root root 4096 Jun 26 06:36 onex drwxr-x---+ 2 root root 4096 Aug  7 21:17 zanna   And, if I do ls -la I get only . and .. in addition to the above, but the count is total 20  What's the explanation? Im working in a site, And I need to present many fields to be filled and the page, so accoding to a selecction before, I have all the field but I have the Api Name, and the object name, but, With this api object field name, how can I get the label????  Example. I have "Student__c", I need to present "Student" to the user.  Thanks a lot for ur help!    Ok, thanks for ur answuers but I think I did not explain well this situation.   I have a list of string, where I have the information but in Api's name.  I present this fields in a table, so the user is filling the fields but with an inputText and not with an inputfield!.. So, in this moment, I dont know what is the label of each field.  My question basically, if by means of a query I could know the label of a field, if I know the api field name and the object name.. My question is if there is a way to consult this info!...  I know if I have the object is enough using an inputfield, But I cant do that. Neither set the label with HTML directly 'cause this is something dynamic.   Anyone knows how can I know, or consult, I guess by means of a query, how to get this label names??? Prove that if $0\le p_n&lt; 1$ and $S=\sum p_n&lt; \infty$ then  $\prod (1-p_n)&gt;0$. Hint given: First show that if $S&lt;1$, then $\prod (1-p_n)\ge 1-S$.   Attempt: I was able to show the hint by using recursion setting $A_n=\prod_{i=1}^{n}(1-p_i)$ re expression the $\prod (1-p_n)$ as $1-S+\sum_{n_1, n_2=1,n_1&lt;n_2 }^{\infty} p_{n_1}p_{n_2}-..... $ and observed that every subsequent term is less than the previous term hence  $\prod (1-p_n)\ge 1-S$ which is $&gt;0$ if $S&lt;1$ but am unsure about how to extend it to $S\ge1$. Compensation for missed connection due to delay with same airline but separate bookings Long story short, I had to fly from A (in Spain) to C (in the UK) and I booked two separate flights with the same budget airline, so the actual route was A (Spain) -> B (UK) -> C (UK).  The first flight was delayed by 90 minutes, which means that I was unable to catch the second one (the layover time was around an hour and a half) and had to buy another ticket for the following day (with another airline).  I googled a lot and found mixed responses. Is there any chance I can get a refund for my second flight? I will obviously ask them but I'm unsure what my best course of action is. How do I give text or an image a transparent background using CSS? Suppose you had a question, and you really want a good answer that would solve your problem, but noticed it was already asked by someone else. However, no one has posted any answers. The question is technically considered "unanswered", but a lot of users who would otherwise bother to give a correct answer probably skip the question completely for some reason.  What should I do in this case?  One idea is to ask a new, completely identical question, in the hope users will notice the new question and post an answer there. But would that go against SE policy?     Note: This is adapted from , but that doesn't cover the case where the original question is unanswered. Also, it is not a duplicate of , as that question asks about getting attention for one's own questions, while this one and the one linked above ask about getting an answer if someone else has already posted the same thing. I have 24 reputation points, but SO chat is still giving me the message "you must have 20 reputation...." Why can't I join the chat? For any matrix $A$, $AA^T$ is symmetric, and thereby diagonalizable (Spectral Theorem). This implies that $AA^T$ has n linearly independent eigenvectors and therefore full rank.  Does this imply that for any matrix $A$, $AA^T$ is always invertible ? I know there is something wrong here because from the above chain we can conclude that a symmetric matrix is always invertible, which is definitely not true.  Could someone please point out where I am going wrong? Let $n$ be an integer, prove that every prime factor of $12x^2+1$ has the form $6m+1$, where $m$ is an integer.  I've gone as far as knowing that all primes $p&gt;3$ are either $6m+1$ or $6m-1$, how do I use this, not sure whether to even use that.  I know about the Legendre symbol and quadratic reciprocity In categorical terms, why is there no canonical isomorphism from a finite dimensional vector space to its dual? I've read in several places that one motivation for category theory was to be able to give precise meaning to statements like, "finite dimensional vector spaces are canonically isomorphic to their double duals; they are isomorphic to their duals as well, but not canonically."  I've finally sat down to work through this, and -  Okay, yes, it is easy to see that the "canonical isomorphism" from $V$ to $V^{**}$ is a functor that has a natural isomorphism (in the sense of category theory) to the identity functor.  Also, I see that there is no way that the functor $V\mapsto V^*$ could have a natural isomorphism to the identity functor, because it is contravariant whereas the identity functor is covariant. My question amounts to:     Is contravariance the whole problem?   To elaborate:   I was initially disappointed by the realization that the definition of natural isomorphism doesn't apply to a pair of functors one of which is covariant and the other contravariant, because I was hoping that the lack of a canonical isomorphism $V\rightarrow V^*$ would feel more like a theorem as opposed to an artifact of the inapplicability of a definition.  Then I tried to create a definition of a natural transformation from a covariant functor $F:\mathscr{A}\rightarrow\mathscr{B}$ to a contravariant functor $G:\mathscr{A}\rightarrow\mathscr{B}$. It seems to me that this definition should be that all objects $A\in\mathscr{A}$ get a morphism $m_A:F(A)\rightarrow G(A)$ such that for all morphisms $f:A\rightarrow A'$ of $\mathscr{A}$, the following diagram (in $\mathscr{B}$) commutes:  $$\require{AMScd}\begin{CD} F(A) @&gt;m_A&gt;&gt; G(A)\\ @VF(f)VV @AAG(f)A\\ F(A') @&gt;&gt;m_{A'}&gt; G(A') \end{CD}$$  This is much more stringent a demand on the $m_A$ than the typical definition of a natural transformation.  Indeed, it is asking that $m_A=G(f)\circ m_{A'}\circ F(f)$, regardless of how $f$ or $A'$ may vary. Taking $\mathscr{A}=\mathscr{B}=\text{f.d.Vec}_k$, $F$ the identity functor and $G$ the dualizing functor, it is clear that this definition can never be satisfied unless $m_V$ is the zero map for all $V\in\text{f.d.Vec}_k$ (because take $f$ to be the zero map). In particular, it cannot be satisfied if $m_V$ is required to be an isomorphism.     Is this the right way to understand (categorically) why there is no natural isomorphism $V\rightarrow V^*$?   As an aside, are there any interesting cases of some kind of analog (the above definition or another) of natural transformations from covariant to contravariant functors?  Note: I have read a number of math.SE answers regarding why $V^*$ is not naturally isomorphic to $V$. None that I have found are addressed to what I'm asking here, which is about how categories make the question and answer precise. ( was closest.) Hence my question here. How to switch 7 wires with a single on/off slide switch I am working on a project, where I want to build a raspberry pi into a nintendo 64 console, and be able to switch between with a single switch. By that I mean, I want to be able to use a single slide switch to either switch on the raspberry, or the n64.   I already figured the most stuff out, but I need help with wiring the controller port.   I have a n64 to USB controller adapter, which is connected to the raspberry. Each controller has 3 pins, VIN, GND and Data. I have 2 ports I need to switch. I also need to switch the usb Power for the raspberry.   So, I need a single switch, which has 2 states (ON, OFF), to switch the n64 controller ports to either the n64 console, or to my USB adapter. It also needs to switch the 2 wire power for the raspberry. I made some pictures to visualize it better:  So here is how it should be for to work with the regular N64. The controller ports are wired to the n64 console, and the raspberry power is not connected.    Then, when you switch it over to work with the raspberry, the n64 controller ports should go to the USB adapter, and the raspberry power is connected.    Now, my problem is I don't know how to achieve that. I know there are slide switches with enough pins, but they have multiple possibilities, not only two.   I also need something small, since the n64 case is small and doesn't have a lot of space.   Any ideas? Add a binary to my path I have an executable. I want to execute the executable in terminal with name only like other commands.  I can put my executable in /usr/local/bin or I could add its PATH to ~/.bashrc. Both will work.  What is better?  Is there  any difference? Benevolent aliens who (initially) refuse to show themselves This is a sci-fi book where aliens arrive on Earth and push Earth towards world peace, but refuse to reveal themselves physically. When the aliens finally do show themselves, we find that they       look like .   I recall that the aliens seemed benevolent, but that humanity did not like the direction they were being told to go. I cannot remember the ending or if the aliens turned out to be truly benevolent. How to scale dimensions proportionally to a specific size? I modeled a man and would like to scale him down to be exactly 6' tall (Z dimension), however I cannot find a way to do that. I know I can go to front ortho view and and use the normal scale S  key to scale it, however that requires some pretty specific fine tuning in order to get it to the right dimensions.  I'd like to be able to essentially type "6" into the Z dimension (don't worry I have it setup in imperial) and have it scale the X and Y dimensions proportionally. I came up some definitions I have sort of difficulty to distinguish. In parentheses are my questions.   $\dfrac {x}{0}$ is Impossible (  If it's impossible it can't have neither infinite solutions or even one. Nevertheless, both $1.$ and $2.$ are divided by zero, but only $2. $ has infinite solutions so as $1.$ has none solution, how and why ?) $\dfrac {0}{0}$ is Undefined and has infinite solutions. (How come one be Undefined and yet has infinite solutions ?) $\dfrac {0}{x}$ and $x \ne 0$, it's okay for me, no problem, but if someone else wants to add something about it, feel free to do it.