I have seen this operation before but cant seem to recall the name or corresponding theory. This operation changes inner product $&lt;a,b&gt; = a^T b$ to $a^T R b$, where $R$ is some matrix. What does this do intuitively and what is the name?
To find out how something is called is the one thing I don't know how to use Google for.  If I have a vector $v$ and a symmetric matrix $H$, then the operation $v^T H v$ gives me some sort of projection of the matrix $H$ on the vector $v$. For example if $H$ is the Hessian, the operation gives me the second derivative in the direction of $v$.  What is the name of this operation?
using gedit through ssh connection - should I have gedit installed on the server? I wanted to try out using graphical tools over ssh. Just to learn a new thing :)  so my understanding is this, I connect like this: ssh -port -x user@server  But I'm running ubuntu server so it has no gui and thus no gui tools. My understanding is I've to install gedit on server. But also xserver?  Can someone clear up this concepts to me? How does the User Card popup work? We are experimenting with enhanced user card mouseover popups and have enabled them network wide. You can tell which users will trigger the popup because they have a 3-D drop shadowy look to their gravatar:    Hover your mouse over the gravatar and wait. Note that the user card mouseover popup will only be displayed if the following conditions are met:   Is the profile complete, and long enough? We enforce a minimum length requirement. The user's reputation must be >= 1k  If you have more links than are able to be displayed after truncation, those extra links will be shown in the bottom of the dialog. We order links at the bottom consistently -- if you include a twitter, google plus, linked in, or facebook those links are prioritized. It will be visible on a question and answer detail page, any page with a list of questions, and the /users list. It will not be shown when a question or answer is wiki'd. It will not be shown when excerpt summary is defined as &lt;!-- summary: &amp;nbsp; --&gt; we support explicitly specifying your user card excerpt summary using the following syntax:  &lt;!-- summary: This is my profile, there are others like it but this one is mine. --&gt;   The above example will result in:    This is now mostly complete.  The goal is allow people to show  off how awesome they are inline, without having to click through to the full user profile page. As far as I know, the variance inflation factor is not computed with pseudo-$R^{2}$ or generalized $R^{2}$ in binary outcome models (e.g. logistic regression).  Are there other measures of multi-colinearity than VIF appropriate to such models?  Why ought or ought not we think about multi-colinearity in such models? Monos in $\mathsf{Mon}$ are injective homomorphisms. Let $f: M \to N$ be a mono in $\mathsf{Mon}$. I want to prove that the underlying function $U(f): U(M) \to U(N)$ is injective.   How can this be done ? Thanks in advance. Once upon a time,  DISPLAY=:0.0 totem /path/to/movie.avi   after ssh 'ing into my desktop from my laptop would cause totem to play movie.avi on my desktop.  Now it gives the error:   No protocol specified Cannot open display:    I reinstalled Debian squeeze when it went stable on both computers, and I guess I broke the config.   I've googled on this, and cannot for the life of me figure out what I'm supposed to be doing.   (VLC has an HTTP interface that works, but it isn't as convenient as ssh.)  The same problem arises when I try to run this from a cron job. note: this question has been updated to reflect that we are currently using MySQL, having done so, I would like to see a how much easier it would be if we switched to a CTE-supporting database.  I have a self-referencing table with a primary key, id and a foreign key parent_id.  +------------+--------------+------+-----+---------+----------------+ | Field      | Type         | Null | Key | Default | Extra          | +------------+--------------+------+-----+---------+----------------+ | id         | int(11)      | NO   | PRI | NULL    | auto_increment |  | parent_id  | int(11)      | YES  |     | NULL    |                |  | name       | varchar(255) | YES  |     | NULL    |                |  | notes      | text         | YES  |     | NULL    |                |  +------------+--------------+------+-----+---------+----------------+   Given a name, how can I query the top-level parent?  Given a name, how can I query all of the id's associated with a record of name = 'foo'?  context: I am not a dba, but am planning to ask a dba to implement this type of hierarchical structure and would like to test some queries. The motivation for doing so is described by .    Here is an example of the relationships among ids in the table:    -- ----------------------------------------------------- -- Create a new database called 'testdb' -- ----------------------------------------------------- SET @OLD_UNIQUE_CHECKS=@@UNIQUE_CHECKS, UNIQUE_CHECKS=0; SET @OLD_FOREIGN_KEY_CHECKS=@@FOREIGN_KEY_CHECKS, FOREIGN_KEY_CHECKS=0; SET @OLD_SQL_MODE=@@SQL_MODE, SQL_MODE='TRADITIONAL';  CREATE SCHEMA IF NOT EXISTS `testdb` DEFAULT CHARACTER SET latin1 COLLATE latin1_swedish_ci ; USE `testdb` ;  -- ----------------------------------------------------- -- Table `testdb`.`observations` -- ----------------------------------------------------- CREATE  TABLE IF NOT EXISTS `testdb`.`observations` (   `id` INT NOT NULL ,   `parent_id` INT NULL ,   `name` VARCHAR(45) NULL ,   PRIMARY KEY (`id`) ) ENGINE = InnoDB;  SET SQL_MODE=@OLD_SQL_MODE; SET FOREIGN_KEY_CHECKS=@OLD_FOREIGN_KEY_CHECKS; SET UNIQUE_CHECKS=@OLD_UNIQUE_CHECKS;  -- ----------------------------------------------------- -- Add Example Data Set -- -----------------------------------------------------   INSERT INTO observations VALUES (1,3), (2,5), (3,NULL), (4,10),     (5,NULL), (6,1), (7,5), (8,10), (9,10), (10,3); Can I choose not to defend against an attack? Playing D&amp;D4e, I have a situation in mind where a character could reasonably WANT to get hit with a normally harmful attack. Is there anything in the rules allowing the character to purposefully take the hit, not even bothering to attempt to defend or dodge out of the way of it?  For example, a dragonborn character makes a breath attack that includes an ally in its blast. The dragonborn has the Nusemnee's Atonement feat, which allows a player whose AOE damages an ally to take the ally's damage instead. This can be paired with a dragonborn feat that recharges your racial dragonbreath power when you take damage of the type it deals. This combination lets the dragonborn recharge their dragonbreath as long as they hit an ally with it. Normally you'd want your ally to at least have a chance to dodge your AOE first, but in this combo, it's best if they can allow themselves to get hit!  Can the ally choose not to defend against the attack, purposefully taking the hit, knowing that the character making the attack will take the damage in his place? When writing answers on here, it's often necessary to create a new script and chmod +x it to make it executable. I won't go into whether this is a good thing or not, but explaining to people that they need to fire in three separate command (and teaching them to use nano!) is a bit of a waffle.  Is there anything easier? evaluate $\int_{0}^{\infty}\cos(t) t^{z-1}dt=\Gamma(z)\cos(\frac{\pi z}{2})$ How does a Pokémon gain CP when evolving? I know this may be a tough or confusing question, but I have numerous existing materials I created and reuse for a project, which were all prepared for Blender Internal.  Now, I want to start the transition to Cycles, but I've hit a roadblock. How can I transition my materials without completely starting over? Or should I just forget it and start with fresh materials? Can we access class properties dynamically with Object class? Is it possible to access Apex class properties dynamically? While we can create Object's, and assign any other class to an Object, I'm not sure how I can access the properties of these Object's. Can anyone provide some documentation or references to code which would allow me to do this?   Example:  public class XYZ {    public string s1 { get; set; }    public string s2 { get; set; } }  XYZ testXyzObj = new XYZ(); Object obj = testXyzObj;  // Method does not exist or incorrect signature: [Object].get(String) String s1 = obj.get('s1'); My background and gameobjects are 2d sprites not UI images ,I want to know how to make my background scale with screen size and positions of 2d sprits on it don't change after building game (webGl) like scale canvas with screen size and anchor points in UI elements .  Before building the game   After building Proving that $ 2 $ is the only real solution of $ 3^x+4^x=5^x $ I would like to prove that the equation $ 3^x+4^x=5^x $ has only one real solution ($x=2$)  I tried to study the function $ f(x)=5^x-4^x-3^x $ (in order to use the intermediate value theorem) but I am not able to find the sign of $ f&#39;(x)= \ln(5)\times5^x-\ln(4)\times4^x-\ln(3)\times3^x $ and I can't see any other method to solve this exercise... In Ruby on Rails, how do I format a date with the "th" suffix, as in, "Sun Oct 5th"? I want to display dates in the format: short day of week, short month, day of month without leading zero but including "th", "st", "nd", or "rd" suffix.  For example, the day this question was asked would display "Thu Oct 2nd".  I'm using Ruby 1.8.7, and  just doesn't seem to do this.  I'd prefer a standard library if one exists. Let's say we are given a set of positive reals, and we're told that these are the edges of a convex  $n$-gon, and we must compute it's area.   For $n = 3$ there is the famous Heron's formula:  $$A = {1\over 4}\sqrt{4a^2b^2 - (a^2 + b^2 - c^2)^2}$$  For $n = 4$ there is Brahmagupta's formula:  $$A = {1\over 4}\sqrt{(a^2 + b^2 + c^2 + d^2)^2 + 8abcd - 2(a^4 + b^4 + c^4 + d^4)}$$  Is there a generalization for arbitrary $n$? Does it even exist? Correct tracked camera orientation How to set the command prompt's color in Bash? How do I enable the "Universe" repository? Should operator<< be implemented as a friend or as a member function? That's basically the question, is there a "right" way to implement operator&lt;&lt; ? Reading  I can see that something like:  friend bool operator&lt;&lt;(obj const&amp; lhs, obj const&amp; rhs);   is preferred to something like   ostream&amp; operator&lt;&lt;(obj const&amp; rhs);   But I can't quite see why should I use one or the other.  My personal case is:  friend ostream &amp; operator&lt;&lt;(ostream &amp;os, const Paragraph&amp; p) {     return os &lt;&lt; p.to_str(); }   But I could probably do:  ostream &amp; operator&lt;&lt;(ostream &amp;os) {     return os &lt;&lt; paragraph; }   What rationale should I base this decision on?  Note:   Paragraph::to_str = (return paragraph)    where paragraph's a string.