Rank of a Matrix Sum
Show $\operatorname{rank}(A) + \operatorname{rank}(B) \ge \operatorname{rank}(A+B)$
How to install Python and wxPython offline? I could not install my modem driver so I have to update and install applications offline. For this I want to use keryx but to install keryx, Python and wxPython have to be installed first. So how do I install Python and wxPython offiline on Ubuntu 13.04?  Note : I don't have internet connection in Ubuntu. So I'll have to download the required file from my Windows 7. Are any of these verb phrases grammatical?        allows the user of modeling and resolving     allows the user to model and resolve      Which version of the following sentence is correct/better?        In particular, it allows to acquire a signal using a sample rate significantly lower than the one dictated by the Nyquist criterion.   In particular, it allows acquiring a signal using a sample rate   significantly lower than the one dictated by the Nyquist criterion.      I searched Google Scholar for "" and "", and it seems people use both more or less with the same frequency. Looping through files with spaces in the names? I wrote the following script to diff the outputs of two directores with all the same files in them as such:  #!/bin/bash  for file in `find . -name "*.csv"`   do      echo "file = $file";      diff $file /some/other/path/$file;      read char; done   I know there are other ways to achieve this.  Curiously though, this script fails when the files have spaces in them.  How can I deal with this?  Example output of find:  ./zQuery - abc - Do Not Prompt for Date.csv I'm a bit confused on how extra damage works for critical hits. Let's take the following example: A thief with sneak attack rolls a crit. I'm under the impression he rolls double his normal attack damage dice AND double his Sneak Attack damage dice. Is this accurate? Another example, I finished DM-ing my first campaign recently. The Giant Spider enemy monster has an melee attack that causes a constitution saving throw. If the player fails, the enemy rolls an additional 2D8 of damage. In this situation, if there was a critical hit, and the player failed their saving throw, would I also roll double dice on the additional damage? Or is that considered a separate attack? Get last result in interactive Python shell Proof Check: Every Cauchy Sequence is Bounded how to run a winform from console application? How do I create, execute and control a winform from within a console application? I've always been confused by the differences in behavior of font commands.  For example, we have \mathrm{} and \texttt{}, which can be used like this: \texttt{hello} world.  And then we have \it and \bf which must be used as {\it hello} world. If one uses \it{hello} world, both words are italicized.  Internally, what is the difference here? And was this difference a conscious design decision? If so, why? Suppose I have a node in the shape of a circle. How can I make its border thicker?   \node[circle, draw=blue!80, inner sep=0pt, minimum size=12pt] (1) at (0,0) {1}; Pearson VS Deviance Residuals in logistic regression I know that standardized Pearson Residuals are obtained in a traditional probabilistic way: $$ r_i = \frac{y_i-\hat{\pi}_i}{\sqrt{\hat{\pi}_i(1-\hat{\pi}_i)}}$$ and Deviance Residuals are obtained through a more statistical way (the contribution of each point to the likelihood): $$ d_i = s_i \sqrt{-2[y_i \log \hat{\pi_i} + (1 - y_i)\log(1-\hat{\pi}_i)]} $$ where $s_i$ = 1 if $y_i$ = 1 and $s_i$ = -1 if $y_i$ = 0. Can you explain to me, intuitively, how to interpret the formula for deviance residuals? Moreover, if I want to choose one, which one is more suitable and why? BTW, some references claim that we derive the deviance residuals based on the term $$-\frac{1}{2}{r_i}^2$$ where $r_i$ is mentioned above. Get month name from Date I currently only have remote access to this CentOS box, I need to move /var form the primary RAID to a new set of disks that was installed with more space, My current thoughts on how to accomplish this is to temporarily mount the new RAID to /tmp/var. rsync everything from /var to /temp/var then modify the fstab to point /var at the new disks.  Here is my question. how do I delete the existing /var on the primary disks once I have the new disks mounted to that location (assuming this is even possible remotely)? What does the origami represent in Blade Runner? Throughout Blade Runner we see Gaff (Edward James Olmos) making origami figures at various points in the movie. He makes a chicken, matchstick men and at the end of the film there is a unicorn waiting outside Deckard's apartment.    There is a   of  out there regarding the unicorn in particular, and how it indicates that Deckard is a replicant. I think an answer regarding the use of origami in general will be interesting new ground to cover.  Why origami? What does the origami represent in Blade Runner? Please explain this put option How can I get a command block? The speed of light as it approaches a massive body No matter how fast you go, you will aways perceive the speed of light as constant. Taking that as a fact, the special relativity theory was formulated. Now, for what I understand about general relativity, just by standing here on the surface of the planet under the effect of gravity, my frame of reference is a little different from someone in geostationary orbit, and time goes by a little slower for me.  So, considering me and someone in geostationary orbit, does both of us would perceive light at the same speed? If so, does that means that the light is slower down here than up there? how to hide mesh but keep hair particles forecast using arima models I am trying to predict values using arima(0,1,1). After doing predict(mod,n.ahead=5) (in R) am getting the same value for all the predictions:   5947.681 5947.681 5947.681 5947.681 5947.681    Is it correct? How to view the moderators here in MSE? I  am able to view the Stack Overflow site moderators by clicking on this    But when I search the same in meta.stackexchange, it does not display the site moderators.    The below message is displayed      We believe moderation starts with the community itself, so in addition   to privileges earned through reputation, we periodically hold   democratic moderator elections.      Please see A Theory of Moderation for information on our moderation   philosophy   My Questions:   Are there restrictions to view the site moderators in meta.Stackexchange? How does the above message make sense when viewing the moderators? Can someone explain this to me? In SQL, what's the difference between count(column) and count(*)?