Determinant of this special matrix
Matrix given by $a_{ij} = 1/(i+j)$ is non-singular.
I have a Google Apps email (me@business.com) set to auto-forward all mail to my personal Gmail (me@gmail.com).  I have added the me@business.com address to my personal Gmail so I can send mail as me@business.com from within my personal email account.  It's a fairly common way to consolidate email accounts.  Here's my problem.  I want me@gmail.com to filter all emails being forwarded from me@business.com and apply the Business label.  So I tried it two different ways:  A) Use an Alias:   me@business.com forward to me+business@gmail.com Create filter "To:me+business@gmail.com" in me@gmail account Have filter apply Business label   B) Use Googlemail.com address:   me@business.com forward to me@googlemail.com Create filter "To:me@googlemail.com" in me@gmail account Have filter apply Business label   However, neither of these filters work.  I've tested it using a third email address, me@yahoo.com.  Whenever I send an email from me@yahoo.com to me@business.com, the email is properly forwarded to me@gmail.com, and I can reply to me@yahoo.com using the me@business.com address.  But Gmail does NOT apply the Business label.  This is case using either filtering method A or B.  But if I send an email from me@yahoo.com DIRECTLY to me+business@gmail.com or me@googlemail.com, the filter works properly and applies the label.  So there must be something going on with the forwarding of me@business.com to me@gmail.com.  Does anyone know how to get this working? Proving that $AB-BA=cI$ for nontrivial $c \in \mathbb{C}$ I have a homework question I can`t solve:  Let $X$ be a normed linear space, $A,B \in B(X)$. Show that there exists no nontrivial $c \in \mathbb{C} $ such that $AB-BA=cI$.  Thanks alot already guys! I seem to have a professor who gives impossible homework problems.  The hint he gave: $A^{n}B-BA^{n}=ncA^{n-1}$, $n \in \mathbb{N}$ Recolor Artwork: single swatch to multiple swatches I have an Illustrator document with a lot of objects. All the objects are black, same swatch.  I have a swatch group with a few dozen coloured swatches. I wish to apply these swatches to all the many black objects. It doesn’t have to be in any particular order, but each object should be coloured individually—I don’t just want to change black into some other colour, but to dozens of other colours. What I really want to avoid is having to select each object individually and then applying a different swatch to each.  I’ve never quite managed to get my head properly around the Recolor Artwork feature in Illustrator, and I cannot for the life of me get it to do anything like this. The “New” box in the Recolor Artwork dialogue box appears to accept only one colour.  Is there some way to do this using the Recolor Artwork feature? Or using some other feature that I’m not aware of? Bonus points if there’s a way to control the order in which the colours are applied; e.g., specifying an order and then click on each object in turn to apply each swatch being ‘iterated’ through in that order.  (I would prefer to avoid having to script it, but I will if there’s no other way.) Hello,   I create an app using the Promoted Links in Sharepoint 2013. I chose to do this because the feature has the awesome hover effect and is easy to customize the image.  The issue is that I have been trying to figure out how to change the tile sizes. They are awesome the way they are, however I just need them smaller. I still want the hover effect as well and for the text to match the same ratio as the tile. I have tried web zones, I have done each ID but with no luck. I have attached a sample image of the tiles I'm referring to. Please help. Identifying which part of a large document is being compiled I got a flat/puncture on my bike tube, how can I fix it myself without going to the nearest bike shop? What kind of equipment would I need? Can I print a custom paper on standsard size in word? SEO safe way to run beta of new site on seperate domain How does centrifugal force work? How can I install packages without starting their associated services? As you're probably aware, by default when you install a package on a Debian or Ubuntu based system, if the package contains a service, that service will generally be enabled and started automatically when you install the package.  This is a problem for me.  I've found myself needing to manage templates for building LXC containers. There are several containers, each corresponding to a Debian or Ubuntu release. (There are also Red Hat-based containers, but they aren't relevant here.)  /var/lib/libvirt/filesystems/debian6_template /var/lib/libvirt/filesystems/debian7_template /var/lib/libvirt/filesystems/ubuntu1004_template /var/lib/libvirt/filesystems/ubuntu1204_template   Occasionally I will find that the templates have a missing package or need some other change, so I will chroot into them to install the package. Unfortunately when I do that, I wind up with several copies of the package's service running!  By way of example, I found the templates didn't have a syslog daemon, so I installed one:  for template in /var/lib/libvirt/filesystems/{debian,ubuntu}*_template; do     chroot $template apt-get install rsyslog done   And promptly wound up with four copies of rsyslog running. Not to mention two copies of exim4. Oops!    I read somewhere (though I can't find it again now) that it's not supposed to start services when running in a chroot, but that clearly isn't happening here.  One potentially viable  calls for temporarily replacing the various commands which actually start services, such as start-stop-daemon and initctl, though this is a lot more work than I really wanted to do. If I have no other choice, though...  The ideal solution here would be for Debian-based systems to stop doing this crap, but failing that, perhaps an obscure or undocumented command line option for apt-get?  In case it wasn't clear, I really want to keep anything related to managing the templates outside the templates, if possible. Are upvotes on competing posts counted per question or per answer for Sportsmanship? The definition of the :     Up voted 100 competing answers   doesn't specify whether each upvote on competing answers to the same question counts towards this criteria, or if it's limited to one "point" per question no matter how many additional competing answers you upvote. Can someone explain how it works? Listing layers from .mxd file using ArcPy for ArcGIS Pro? I compile most of my documents via Makefiles which take care of the bibliography, indexes, etc. Often I'd like to compile different versions from the same TeX file changing only small things (e.g. a beamer presentation plus a version with the handout option).  Is there any standard mechanism for passing parameters to the TeX file so that I can just type make handout to get the handout version in the above example? Do gravitons interact with each other? I always thought the non-linearity of Einsteins field equations implies that there should be direct graviton-graviton interactions. But I stumbled upon  which argues:     If gravitons exist, then, like photons and unlike gluons, gravitons do   not interact with other particles of their kind. That is, gravitons   carry the force of gravitation but are not affected by it. This is   apparent due to gravity being the only thing which escapes from black   holes, in addition to having an infinite range and traveling in   straight lines, similarly to electromagnetism.   Is Wikipedia correct? If not, why not? And what then are the arguments that there must be graviton-graviton interactions?    (As of this question being asked, the above paragraph has been removed from Wikipedia.) Can I choose which damage type my Sneak Attack does if my weapon does multiple types? Note that this is only focusing on Minecraft Java Edition, and for versions 1.13+. I am predominantly looking for a solution that does not require any external programs (like MCEdit or NBTExplorer) and will work in just plain vanilla Minecraft, although if the only solution doesn't fit these criteria, I'll still take it (since having a solution is better than no solution!) Essentially, I am looking for a way to put a phrase (meaning essentially there are two or more words and spaces are involved) on a Minecraft scoreboard. This is what I mean by 'phrase': One two three, 1 2 3 These are not 'phrases': OneTwoThree, One-Two-Three, One_Two_Three, 1-2-3, etc. However, it seems like the only way to add text to an objective on the scoreboard is to add a &quot;fake player&quot;, via /scoreboard  players add [playername] [objectivename] [score], which shows the [playername] and the [score] part of the command on the scoreboard. However, since player names can't have spaces at all, it means that you can't have a phrase shown on the scoreboard. I have seen on many servers scoreboards that do have phrases listed on the scoreboard, but I have no idea how they do this (probably because of plugins that can do this sort of thing).  I did notice that teams can be given display names that can have spaces, so is there a way to display the team name on the scoreboard (thus being able to put phrases on there?)? Overall, my main question would be &quot;Is there a way to use spaces on the scoreboard (excluding the objective name) in vanilla Minecraft? In the new canon what do we actually know about Darth Plagueis? I read and loved  but with all the recent changes to what is and isn't canon I'm losing track.  There's a common theory that Supreme Leader Snoke is Darth Plagueis, most are discounted because Plagueis is a Muun. But where does that information come from? What current canon information do we have about Plagueis that disproves this theory and what has been marked as Legends? I have a repeated composition of functions ${T_n}(z) = {\tau _0} \circ {\tau _1} \circ {\tau _2} \circ  \cdots  \circ {\tau _n}(z)$  By analogy with $\sum\limits_{i = 1}^n {} ,\prod\limits_{i = 1}^n {} ,\bigcup\limits_{i = 1}^n {} ,\bigcap\limits_{i = 1}^n {} ,$ I want to write ${T_n}(z) = \left( {\mathop  \circ \limits_{i = 0}^n {\tau _i}} \right)(z)$ or even ${T_n}(z) = {\mathop  \circ \limits_{i = 0}^n {\tau _i}} (z)$. Can I do this? XGBoost Loss function Approximation With Taylor Expansion As an example, take the objective function of the XGBoost model on the $t$'th iteration:  $$\mathcal{L}^{(t)}=\sum_{i=1}^n\ell(y_i,\hat{y}_i^{(t-1)}+f_t(\mathbf{x}_i))+\Omega(f_t)$$  where $\ell$ is the loss function, $f_t$ is the $t$'th tree output and $\Omega$ is the regularization. One of the (many) key steps for fast calculation is the approximation:  $$\mathcal{L}^{(t)}\approx \sum_{i=1}^n\ell(y_i,\hat{y}_i^{(t-1)})+g_tf_t(\mathbf{x}_i)+\frac{1}{2}h_if_t^2(\mathbf{x}_i)+\Omega(f_t),$$  where $g_i$ and $h_i$ are the first and second derivatives of the loss function.   What I'm asking for is convincing arguments to demystify why the above approximation works:  1) How does XGBoost with the above approximation compare to XGBoost with the full objective function? What potentially interesting, higher-order behavior is lost in the approximation?  2) It's a bit hard to visualize (and depends on the loss function) but, if the loss function has a large cubic component, then the approximation will likely fail. How is it that this doesn't cause problems for XGBoost? Metropolis is not working I tried to use the metropolis beamer theme, but I got the following error  ! Package beamerfontthememetropolis Error: Patching section title failed. See the beamerfontthememetropolis package documentation for explanation. Type H &lt;return&gt; for immediate help.... \patchcmd