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What is the difference between \em and \emph? What is the difference between \emph{...} and {\em ...}?  When to use each of them? Does Reincarnation allows skills to be passed into other classes I'm mainly asking this for Disgaea: Afternoon of Darkness, given I have enough Mana to reincarnate a character into 4 different types of Mages (Green, Blue, Red, Star), a Cleric and then a Warrior, would the Warrior have all the spells learned from the previous classes? Why are symmetric positive definite (SPD) matrices so important? I know the definition of symmetric positive definite (SPD) matrix, but want to understand more.   Why are they so important, intuitively?  Here is what I know. What else?   For a given data, Co-variance matrix is SPD. Co-variance matrix is a important metric, see this  for intuitive explanation. The quadratic form $\frac 1 2 x^\top Ax-b^\top x +c$ is convex, if $A$ is SPD. Convexity is a nice property for a function that can make sure the local solution is global solution. For Convex problems, there are many good algorithms to solve, but not for non-covex problems. When $A$ is SPD, the optimization solution for the quadratic form $$\text{minimize}~~~ \frac 1 2 x^\top Ax-b^\top x +c$$ and the solution for linear system $$Ax=b$$ are the same. So we can run conversions between two classical problems. This is important because it enables us to use tricks discovered in one domain in the another. For example, we can use the conjugate gradient method to solve a linear system.  There are many good algorithms (fast, numerical stable) that work better for an SPD matrix, such as Cholesky decomposition.   EDIT: I am not trying ask the identities for SPD matrix, but the intuition behind the property to show the importance. For example, as mentioned by @Matthew Drury, if a matrix is SPD, Eigenvalues are all positive real numbers, but why all positive matters. @Matthew Drury had a great answer to flow and that is what I was looking for. Differentiability implying continuity Theorem: If $f$ is finitely differentiable at $c$, then $f$ is also continuous at $c$.  But according to the definition, for a function to be differentiable at $c$, it need not even be defined at $c$, just that it should have a finite value in the vicinity of $c$.    My question: If function is not defined at $c$, how can it be continuous at $c$?  For example, say we have a straight horizontal line function which is broken at $x=1$, the function is defined at all the points except $x=1$, it has a finite value at all the points except $x=1$, since it is having a value in the nearby region of $x=1$ we say that it is differentiable at $x=1$ but can we say that it is continuous at $x=1$? Can't connect to wireless networks on a Dell Latitude D430 As stated above, I can't connect to my home wi-fi with natty but can with Windows 7. The strange thing is I that I have gotten it to connect to other password protected networks with natty, it's just mine that it dosn't like.   I am using a WPA2 pass-code with AES Encryption and all other devises work fine on my network. Laptop used is a Dell Latitude D430. I've tried different ways to install iTunes, but to no avail. I tried with Wine, but it didn't work. Is it possible to have iTunes on Ubuntu? Windows Spotlight Source and Save locations? Where are the images from  coming from?  Where are they being saved on my system?  Is there any way for me to point this at my own source of images? Appendix in LaTeX Is it possible to smooth or generalize a polygon in QGIS, perhaps by using a plugin like the generalizer-plugin for lines?  I could convert my polygons to lines, smooth them and convert them back to polygons but this is not working for my polygons because of several reasons. How to add greek polytonic with setxkbmap I want to add greek polytonic keyboard layout under Lubuntu (so in LXDE). I already realized there is no easy tool to do it with the graphic interface, so I need to use setxkbmap executing something the like of:  setxkbmap pl,gr   Now, how to make setxkbmap set the greek polytonic variant? Does the derivative of a continuous function goes to zero if the function converges to it? The number of different ways to choose $k$ out of $n$ unique items The number of different ways to choose $k$ out of $n$ unique items:   Without repetition and without order-significance: $\binom{n}{k}=\frac{n!}{k!(n-k)!}$ Without repetition and with order-significance: $\binom{n}{k}\times k!=\frac{n!}{(n-k)!}$ With repetition and with order-significance: $n^k$ With repetition and without order-significance: $?$   Thank you! Is there an exact command for restarting GNOME Shell in Ubuntu 20.04 corresponding to Alt + F2 + 'r' + Enter? Is there a way to restart GNOME Shell other than by using Alt + F2, R + Enter? With respect to the question, I have gone through , but I didn't get what I was looking for. I am looking for a command which exactly does what Alt + F2, r + Enter do. Please note that I am not willing to do the gnome-shell -- replace command... I did check both the things Alt + F2,r Enter and gnome-shell --replace... There is a lot of difference, I found... With a two-party system, our nation will divide the people (who/whom)   most need to be brought together.   Do I use who or whom for this sentence?  I think that "people" is the direct object and warrants the use of "whom", but I want to make sure I'm right. Can I color text by using an image, so that the color isn't flat? I'm using tikz to attempt to make a book cover, and I have a "wallpaper" image that looks like leather (not that I've handled that many leather-bound books). I'm using the node command to place text over the top of it, but none of the colors I've experimented with look decent.  Can I use an image of gold-leaf as the fill/stroke for the text? Or for that matter, for the path lines as well?  I've tried googling for this, but I can't figure out a set of keywords non-generic enough to pull back useful results. Shimano Deore front derailleur occasionally sticking I have a question about my front derailleur sticking occasionally.  I've had this bike for a 1.7 years and have ridden it through 2 winters.  It has only been after this last winter that my front derailleur has been sticking on occasion where it's like grit has jammed in somewhere (which I'm sure it is the case).  When I'm on the fly I just knock it with my heel and it will downshift and I can push the shifter hard enough to go back up when I need to.  The first time I decided to overhaul both the front and back ones.  Took them apart, cleaned/degreased, regreased the two back cogs, and used WD-40 professional silicone on the rest of the parts as to not attract more dirt.  Then after about a month it got stuck again, and I couldn't see anything that could be jamming it (while it was still stiff as heck).  Didn't take it apart this time just used a tooth brush and silicone again and it's fine at the moment.  I'm assuming it may be that since that the roads have been grittier/dirtier from the winter with some recent rain and slush that it may just be normal.  I haven't been on the trails yet this year so I know it's not that.  Is this normal, has some kind of bur that I can't see come up and is catching grit?  EDIT:  I should also note that this is a hardtail mtb that I use for trails and winter commuting (a lot of salt and grit on the roads). How can I tell which version of Windows 8 I am running? Standard, Pro, Enterprise, or RT? I have searched everywhere but cannot find how to tell which version of Windows 8 I am running.  I have the system properties on the screen but it just says "Windows 8," nothing else.  Is this the standard edition?  EDIT 04142015:  My new favorite way to do this is to go to the commnand prompt and issue (same with Windows 7):    wmic os get caption  Response:  Microsoft Windows 8.1 Pro Prove that $\sqrt 2 + \sqrt 3$ is irrational I have proved in earlier exercises of this book that $\sqrt 2$ and $\sqrt 3$ are irrational. Then, the sum of two irrational numbers is an irrational number. Thus, $\sqrt 2 + \sqrt 3$ is irrational. My first question is, is this reasoning correct?  Secondly, the book wants me to use the fact that if $n$ is an integer that is not a perfect square, then $\sqrt n$ is irrational. This means that $\sqrt 6$ is irrational. How are we to use this fact? Can we reason as follows:  $\sqrt 6$ is irrational  $\Rightarrow \sqrt{2 \cdot 3}$ is irrational.  $\Rightarrow \sqrt 2 \cdot \sqrt 3$ is irrational  $\Rightarrow \sqrt 2$ or $\sqrt 3$ or both are irrational.  $\Rightarrow \sqrt 2 + \sqrt 3$ is irrational.  Is this way of reasoning correct? I have a set of polygons representing administrative districts.  The districts were digitized by hand, and there are small spaces (slivers) between polygons where the polygons should be touching. How can I have the polygons snap together, removing the spaces? As of late, and without my deliberately doing anything to make it happen, my Bash prompt has an  (i.e. @) prepended to it. This did not previously happen. Nor can I see anything in my ~/.bashrc that seems as though it ought to be making this happen.  This is on Debian Jessie GNU/Linux, using GNU Bash.  For example, my current Bash sessions look like this:  @sampablokuper@debianbox:~$ python3 Python 3.4.2 (default, Oct  8 2014, 13:14:40)  [GCC 4.9.1] on linux Type "help", "copyright", "credits" or "license" for more information. @&gt;&gt;&gt; 1+2 3 @&gt;&gt;&gt; exit() @sampablokuper@debianbox:~$    whereas originally, they would have looked like this:  sampablokuper@debianbox:~$ python3 Python 3.4.2 (default, Oct  8 2014, 13:14:40)  [GCC 4.9.1] on linux Type "help", "copyright", "credits" or "license" for more information. &gt;&gt;&gt; 1+2 3 &gt;&gt;&gt; exit() sampablokuper@debianbox:~$    Here are all the lines from my ~/.bashrc that appear to in any way relate to the Bash prompt:  # set variable identifying the chroot you work in (used in the prompt below) if [ -z "${debian_chroot:-}" ] &amp;&amp; [ -r /etc/debian_chroot ]; then     debian_chroot=$(cat /etc/debian_chroot) fi  # set a fancy prompt (non-color, unless we know we "want" color) case "$TERM" in     xterm-color) color_prompt=yes;; esac  # uncomment for a colored prompt, if the terminal has the capability; turned # off by default to not distract the user: the focus in a terminal window # should be on the output of commands, not on the prompt #force_color_prompt=yes  if [ -n "$force_color_prompt" ]; then     if [ -x /usr/bin/tput ] &amp;&amp; tput setaf 1 &gt;&amp;/dev/null; then         # We have color support; assume it's compliant with Ecma-48         # (ISO/IEC-6429). (Lack of such support is extremely rare, and such         # a case would tend to support setf rather than setaf.)         color_prompt=yes     else         color_prompt=     fi fi  if [ "$color_prompt" = yes ]; then     PS1='${debian_chroot:+($debian_chroot)}\[\033[01;32m\]\u@\h\[\033[00m\]:\[\033[01;34m\]\w\[\033[00m\]\$ ' else     PS1='${debian_chroot:+($debian_chroot)}\u@\h:\w\$ ' fi unset color_prompt force_color_prompt  # If this is an xterm set the title to user@host:dir case "$TERM" in xterm*|rxvt*)     PS1="\[\e]0;${debian_chroot:+($debian_chroot)}\u@\h: \w\a\]$PS1"     ;; *)     ;; esac   How can I get my Bash prompt to appear as it did originally?