Why are the directions of eigenvectors in SVD and Eigen-Decomposition for PCA opposite?
I'm getting "jumpy" loadings in rollapply PCA in R. Can I fix it?
Understanding the difference between two theorems related to $|G\,:\,K|=|H\,:\,K|\cdot|G\,:\,H|$. Retrieving Maxwell's equations from the minimum action principle Prove that in a triangle $$r^2+r_1^2+r_2^2+r_3^2=16R^2-(a^2+b^2+c^2)$$ where the symbols have their usual meanings. I am looking for a smaller or elegant proof using trigonometry. A geometric proof would be super cool. I did prove it but it took me ages to do the calculation. Thanks. Cartographic techniques for symbolizing routing data External program from our Java program How can I write a program in Java that will execute another program? Also, the input of that program should be given from our program and the output of that program should be written into a file.  This is my small set of code to get its output:  Process p = Runtime.getRuntime().exec("C:\\j2sdk1.4.0\bin\\helloworld.java"); BufferedReader input =         new BufferedReader(new InputStreamReader(p.getInputStream())); while ((line = input.readLine()) != null)    System.out.println(line);  input.close();   This was my set of code but this throws an IOException. How do I get the next element in HTML using JavaScript?  Suppose I have three &lt;div&gt;s and I get a reference to one in JavaScript code, I want to get which is the next &lt;div&gt; and which is the previous. Can I ever go wrong if I keep thinking of derivatives as ratios? Active login not recognized on Super User Locking a file in Python Daily review limit exceeded I have just reached my limit of suggested edits for the day when I noticed someone else has 21, when the limit is 20, how can this be? "no public key available" on apt-get update Integral change that I don't understand If $f(t)$ is a Probability density function of a positive RV.  $\int_0^\infty\int_x^{\infty}f(t)dtdx$ Using fubini theorem should become $\int_0^\infty\int_0^{t}f(t)dxdt$  But why? Surely the answer is very simple but I don't see it. Fubini theorem allows the change of the order of integration. So it should become $\int_0^\infty\int_x^{\infty}f(t)dxdt$  but then I don't understand what meaning could have $\int_x^{\infty}dx$ It seems that a number of the statistical packages that I use wrap these two concepts together. However, I'm wondering if there are different assumptions or data 'formalities' that must be true to use one over the other. A real example would be incredibly useful. Convert line voltage heating system to use low voltage thermostats I currently have two line voltage ceiling radiant heating systems in my condo each with their own DPST thermostat. I'd like to use low voltage thermostats such as the nest. I found , but it only has 3 wires. Will this work with a system designed to use DPST thermostats? If not, is there something else out there that will allow me to use low voltage thermostats with line voltage heaters? Why is mathematical induction a valid proof technique? running rmi server, classnotfound How do we explain the behavior of \rput, \psGetNodeCenter and saveNodeCoors? Introduction  I am writing a tutorial on a short introduction to PSTricks for newbies. I got obstacles to explain how  a node A (for example), \rput, (!\psGetNodeCenter{A} A.x A.y) and (!N-A.x N-A.y) work by design.  I have read the pst-node documentation as shown below.      And the following is taken from page 35-36:    The manual says:   The transformation matrix will be reset by \psGetNodeCenter. (!N-A.x N-A.y) is not affected by \rput.   Even though I read it many times, I still get confused. The statements are too short.  Problem  Please consider the following figure for the remaining discussion.     Case 1  A node A is defined outside \rput and a dot is translated by \rput.   with (!\psGetNodeCenter{A} A.x A.y)  \pnode(2,2){A} \rput(1,1){\psdots(!\psGetNodeCenter{A} A.x A.y)}  with (!N-A.x N-A.y)  \pnode(2,2){A} \rput(1,1){\psdots(!N-A.x N-A.y)}    The results are different. \rput only affects (!N-A.x N-A.y). Case 2  A node A is defined inside \rput and a dot is translated by \rput.   with (!\psGetNodeCenter{A} A.x A.y)  \rput(1,1){\pnode(2,2){A}\psdots(!\psGetNodeCenter{A} A.x A.y)}  with (!N-A.x N-A.y)  \rput(1,1){\pnode(2,2){A}\psdots(!N-A.x N-A.y)}    The results are identical. \rput affects both. Case 3  A node A is defined inside \rput and a dot is defined outside \rput.   with (!\psGetNodeCenter{A} A.x A.y)   \rput(1,1){\pnode(2,2){A}}  \psdots(!\psGetNodeCenter{A} A.x A.y)  with (!N-A.x N-A.y)   \rput(1,1){\pnode(2,2){A}}  \psdots(!N-A.x N-A.y)    The results are different. \rput only affects (!\psGetNodeCenter{A} A.x A.y).   The MWE is given as follows.  \documentclass[margin=12pt]{standalone} \usepackage{pst-node} \addtopsstyle{gridstyle}{gridlabels=5pt} \psset{saveNodeCoors,linecolor=red} \everypsbox{\color{blue}} \begin{document}  \begin{psmatrix} \begin{pspicture}[showgrid=bottom](3,3)     \rput(1,1){Case 1-A}     \pnode(2,2){A}     \rput(1,1){\psdots(!\psGetNodeCenter{A} A.x A.y)} \end{pspicture} &amp; \begin{pspicture}[showgrid=bottom](3,3)     \rput(1,1){Case 1-B}     \pnode(2,2){A}     \rput(1,1){\psdots(!N-A.x N-A.y)} \end{pspicture} \\ % case 2 \begin{pspicture}[showgrid=bottom](3,3)     \rput(1,1){Case 2-A}     \rput(1,1){\pnode(2,2){A}\psdots(!\psGetNodeCenter{A} A.x A.y)} \end{pspicture} &amp; \begin{pspicture}[showgrid=bottom](3,3)     \rput(1,1){Case 2-B}     \rput(1,1){\pnode(2,2){A}\psdots(!N-A.x N-A.y)} \end{pspicture} \\ % case 3 \begin{pspicture}[showgrid=bottom](3,3)     \rput(1,1){Case 3-A}     \rput(1,1){\pnode(2,2){A}}     \psdots(!\psGetNodeCenter{A} A.x A.y) \end{pspicture} &amp; \begin{pspicture}[showgrid=bottom](3,3)     \rput(1,1){Case 3-B}     \rput(1,1){\pnode(2,2){A}}     \psdots(!N-A.x N-A.y) \end{pspicture} \end{psmatrix} \end{document}   Question  How do I have to explain their behaviors to the newbies as the statements in the documentation seem to be unclear?  Note: As (!\psGetNodeCenter{A} A.x A.y) is identical to (A), (A) will not be discussed here.     If you are a teacher, how do you explain it to your   students? INT(5) vs SMALLINT(5): numbers in parenthesis after the numeric type When is $f_{xy}(x,y)\neq f_{yx}(x,y)?$ When is $f_{xy}(x,y)\neq f_{yx}(x,y)?$, where $f_{xy}$ and $f_{yx}$ denote the mixed (second) partial derivatives of a multivariable function $z=f(x,y)$. How can I disable Alt-Scroll zoom in XFCE4 (Xubuntu) In XFCE4 desktop environments, alt+scroll wheel zooms my entire desktop. I'm finding this very annoying because sometimes I flick the scroll wheel to go to the top of a document then press the alt key for a some unrelated keyboard shortcut and find myself zoomed in so far I can't see anything at all. Is there any way to disable this feature?