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What is the geometric meaning of the determinant of a matrix? I know that "The determinant of a matrix represents the area of ​​a rectangle." Perhaps this phrase is imprecise, but I would like to know something more, please.  Thank you very much. Math notation in LaTeX? How can I write e^(3j) in LaTeX?  I have tried many syntax, like $e^(3j)$ or $e^*{3j}$  Any help will be very well received. How to fix "W: Duplicate sources.list entry"? Path connected space that is not locally connected How I can identify which process is making UDP traffic on Linux? Display keyboard without animation Identity for convolution of central binomial coefficients: $\sum\limits_{k=0}^n \binom{2k}{k}\binom{2(n-k)}{n-k}=2^{2n}$ It's not difficult to show that  $$(1-z^2)^{-1/2}=\sum_{n=0}^\infty \binom{2n}{n}2^{-2n}z^{2n}$$  On the other hand, we have $(1-z^2)^{-1}=\sum z^{2n}$.  Squaring the first power series and comparing terms gives us  $$\sum_{k=0}^n \binom{2k}{k}\binom{2(n-k)}{n-k}2^{-2n}=1$$  that is,  $$\sum_{k=0}^n \binom{2k}{k}\binom{2(n-k)}{n-k}=2^{2n}$$  My question: is there a more direct, combinatorial proof of this identity?  I've been racking my brains trying to come up with one but I'm not having much success. Is there a definition of  and proper explanation of it?  It is said "Electric charge is the physical property of matter that causes it to experience a force when close to other electrically charged matter."  How is it though that matter can get charged?  Defining charge as the property of feeling a force with other charged matter seems circular.  What is charge?  Is there a non-circular definition / explanation? Suppose there are two users that have commented on an answer. Both have the same user name, and I want to reply to one of them. How can I do this?  It appears that, under the current system, there is no way for me to do this. Specifically, from , I see that:     4. Matching is performed in reverse chronological order, so if five people named John are participating, @john will match the most recent John   So, consider this a request to add this feature using an -n suffix or something similar; e.g. @john-2 could be used to reply to the second John from the top.  Update Thanks to  for nice answer of @name(userid) based auto-complete suggestion which has no loophole. It involves no counting from top &amp; has no consequences when a comment is deleted. But, I think @name(userid) should be used directly in comment as all form inputs at SE are text (nothing embedded).  Now, I'm trying to finalize it based on it: The system should allow optional @name(userid) format for reply. Provided userid with this format, system should ignore name. And, in the situation of duplicate name based confusion, system should demand this format as mandatory to submit comment.  How to get userid? In case of duplicate name based confusion, system should append (userid) in hypertext to their profile. It'd work for mobile version too. On full version, for easy fill-up, a hover reply icon would be fine (like hover vote up icon). Upon clicking it, system should fill @name(userid) in comment text box.  From reply reader side: Multiple Johns could be confused even if they didn't come from notification (because nobody remembers his/her own userid). So, highlight the background of comments which are replied to them. How to distinguish Nexus 7 (2012) and Nexus 7 (2013) I am having trouble with Bluetooth Low Energy (BT 4.0) on a Nexus 7.  I think I may have a 2012 model.  How to tell if I have a 2012 or 2013 version of the Nexus 7? I'm too spoiled by Windows utilities that take a digital snapshot of your entire drive, which you can then restore from in the event of a drive crash.  (e.g. like Time Machine for Mac OS X).  Is there a similar way of doing this in Linux? Order of products of elements in a finite Abelian group Does Earth's Rotation Affect Its Shape? The question I am working on is, &quot;Consider the following. (a) Find the angular speed of Earth's rotation about its axis. rad/s (b) How does this rotation affect the shape of Earth?&quot;  I am fully capable of solving part (a); however, I am not sure how to describe the effect earth's rotation on its shape. I tried to search my textbook for the answer, but could not find anything. Is there an actual effect on the shape? What is the difference between "why are you worried" and "why you are worried"? Is GNU's Java Compiler (GCJ) dead? Wifi hotspot software package other than ap-hotspot? How to automatically keep user remembered in Devise How to disable the "highlight changes" feature? Our admins deployed a new version of Notepad++ (version 6.3) on our machines, and this version is highlighting all changes done in a file by default. It does so by setting the background color of every modified line to a bright orange, which I find very distracting.  We  have dozens of plugins installed, but I double checked and we do not have the "Change Markers" plugin (which could be the culprit).  Any idea where I can disable this feature? Changing the highlight color could also be an option. I want to find all files which contain a specific string of text. The grep command works, but I don't know how to use it for every directory (I can only do it for my current directory). I tried reading man grep, but it didn't yield any help. Should "each" be followed by a singular or plural possessive? If a possessive noun, which is plural, is preceded by "each", then should it use the singular or plural possessive form?  For example, which of the following is correct?    spend time in each other's presence spend time in each others' presence