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What's the relationship between initial eigenvalues and sums of squared loadings in factor analysis? On the one hand I read in a comment  that:     You can't speak of "eigenvalues" after rotation, even orthogonal   rotation. Perhaps you mean sum of squared loadings for a principal   component, after rotation. When rotation is oblique, this sum of   squares tells nothing about the amount of variance explained, because   components aren't orthogonal anymore. So, you shouldn't report any   percentage of variance explained.   On the other hand, I sometimes read in books people saying things like:     The eigenvalues associated with each factor represent the variance   explained by that particular factor; SPSS also displays the eigenvalue   in terms of the percentage of variance explained (so factor 1 explains   31.696% of total variance). The first few factors explain relatively large amounts of variance (especially factor 1), whereas subsequent   factors explain only small amounts of variance. SPSS then extracts all   factors with eigenvalues greater than 1, which leaves us with four   factors. The eigenvalues associated with these factors are again   displayed (and the percentage of variance explained) in the columns   labelled Extraction Sums of Squared Loadings.   That text is from Field (2013) Discovering statistics using IBM SPSS, and this diagram accompanies it.    I'm wondering     Who is correct about whether it's possible to speak of eigenvalues after rotation? Would it matter if it was an oblique or orthogonal rotation?   Why are the "initial eigenvalues" different from the "extraction sums of squared loadings"? Which is a better measure of total variation explained by the factors (or principal components or whatever method is used)? Should I say that the first four factors explain 50.317% of variation, or 40.477%? Quotient ring of a localization of a ring Let $A$ be a commutative ring. Let $P$ be a prime ideal of $A$. Let $I$ be an ideal of $A$ such that $I \subset P$. Let $\bar A = A/I$. Let $\bar P = P/I$. Is $\bar A_{\bar P}$ isomorphic to $A_P/IA_P$? I have a polygon layer in QGIS, and would like to represent the polygons like in the below image:    I have tried two different approaches, none of which are satisfactory.    Using a line pattern fill, the entire polygon is filled with the line pattern. I need a blank area in the middle which is not filled in.    Using a marker line fill, I am able to keep a blank area in the middle, but the markers are rotated to align with the edges of the polygon. I need the markers to preserve the same rotation along all edges, like in the example above.  Any ideas? elementary row operation change the eigenvalue of a matrix I know that elementary row operations may change the eigenvalues of a matrix, but if these operations don't change the determinant, why should change the eigenvalues??  Thanks In order to animate a character so that it grabs an object an throws it, I added a Child-Of constrained and keyframed its influence. In the F-curve Editor I can't set the curve which controls the influence to interpolation-mode Constant without changing the other curves (Which should be linear or bezier).   How can the interpolation mode of a curve changed independently? Understanding relation between Quotient Space and $S^1$ There is this example at the Wikipedia article on Quotient spaces (QS):     Consider the set $X = \mathbb{R}$ of all real numbers with the ordinary topology, and write $x \sim y$ if and only if $x−y$ is an integer. Then the quotient space $X/\sim$ is homeomorphic to the unit circle $S^1$ via the homeomorphism which sends the equivalence class of $x$ to $\exp(2πix)$.   I understand relations, equivalence relation and equivalence class but quotient space is still too abstract for me. This seems like a simple enough example to begin with.  I understand (sort of) the definition but I can't visualize. And by this example and others, there is a lot of visualizing going on here! torus, circles etc. Why cant we replace diode connected BJTs by simple diodes in a current mirror circuit? Where is the precmd command in android? I'm kind of used to linux. I'm using Busybox from the Busybox Free installer, with Busybox 1.21.0-Stericson. Trying to chance my shell to the Busybox shell using busybox ash gives the following error after every single command:  ash: precmd: not found echo $PS1 $(precmd)$USER@$HOSTNAME:${PWD: -?} $    I tried to go back to the normal shell and find out WHERE precmd is:  which precmd   It just changes the prompt to have "1|" in front of it, without giving me WHERE it is. I found a solution , but have no idea where to put it. I'm basically trying to do the same as  (make Busybox shell the default). Is there a general theorem stating why the restricted Lorentz group's exponential map is surjective? The exponential map for the restricted Lorentz group is surjective. An outline of why is shown on the wiki page .  Is there a more general theorem that states that for some class of Lie groups or Riemannian manifolds (which includes the restricted Lorentz group), the exponential map is surjective?  There is a theorem stating that compact, connected Lie groups have surjective exponential maps. But as the restricted Lorentz group is not compact, this isn't applicable. How do I read / convert an InputStream into a String in Java? How to reset the terminal properties and preferences? How can the pixel values of a raster image be extracted under a polygon fishnet? I'm having trouble solving a Fitch Style Proof and I was hoping someone would be able to help me.  Premises: p ∧ q  Goal: q ∨ r  Would be an assumption (p ∧ q => q ∨ r) in first step a correct one?   Then, q ∨ r Implication Elimination: 2, 1  Why is it not correct?  Thank you very much for any help! I know this sounds like a stupid question, but I just wanted to confirm if they are the same thing. In new canon, anti-gravity is never mentioned. I have a production server running with the following flag: -XX:+HeapDumpOnOutOfMemoryError  Last night it generated a java-38942.hprof file when our server encountered a heap error. It turns out that the developers of the system knew of the flag but no way to get any useful information from it.  Any ideas? Prove that: area of triangle $S_{ABC}=p \cdot R$, where p is half perimeter of triangle $DEF$ Prove that: area of triangle $S_{ABC}=p \cdot R$, where p is half perimeter of triangle $DEF$. $AD,CF, BE$ are altitudes. Is there a simple way? Is it ok to say "good morning" at anytime? elementary row operation change the eigenvalue of a matrix In-Page Editor Line Distortion The SFDC In-page editor has always had distortion for me, and I'm just wondering if it's just a lousy browser plugin they're using or if someone has found a good browser / operating system combination that stops the obnoxious distortion.   Obviously Salesforce doesn't have much interest in fixing it: as it's been this way on multiple operating systems and browsers I've used since I've used Salesforce.  However, my frustration with their other developer tools has lead me to use it occasionally and it's always the same: SqlException from Entity Framework - New transaction is not allowed because there are other threads running in the session