I am trying to prove this statement. I am assuming that if a 3x3 matrix always has an eigenvector, then it also always has an eigenvalue. I tried to prove this looking at a general 3x3 case and trying to calculate det(A-$\lambda$I)=0, but it does not get me anywhere. Is there something intuitive that I am missing?
what do it mean by "A real nxn matrix always has a real eigenvalue when n is odd?" Shouldnt it be that regardless of odd or even there will always have a real root?  hope to hear from you guys soon:)
Possible Duplicate:          Is there anywhere or anyone to complain to about the behaviour of moderators? I've been "spoken" to offensively by a moderator, and I'm unhappy about it. How to combine paths in Java? Is there a Java equivalent for  in C#/.NET? Or any code to accomplish this?  This static method combines one or more strings into a path. What happens if I buy a game I already own through Steam a second time? I am debating whether or not to get the Potato Sack (yes, I realize I've been debating for several weeks now) bundle through steam.  I already own: Defense Grid: The Awakening, Super Meat Boy, and Audiosurf, all of which are part of the sack pack. What happens if I buy the Potato Sack?  Do I get 2nd copies of the three above mentioned games to gift elsewhere?  Is the price of the bundle reduced by the games I already have?  Do I get nothing special for already owning those 3 games? What are the browser and resolution stats for SO users? Google Analytics (and some log parsers) will give you breakdowns on usage of different browsers, different versions of those browsers and screen resolutions.  I'm just curious to know what SO users user. Any chance we could get some stats on that? You may view this as commercial information, in which case I understand (as i'ts relevant to marketing/advertising).  I'm also curious to know the # of users who read and/or post from mobile devices and if so which ones.  UPDATE: Please refrain from personal anecdotes ("I use..."). I'm interested in actual usage, not personal stories. Thankyou. I am using \if condition in a custom command in my LaTeX document. I would like to know where I can find some good explanation about \if command. I followed a  but it's just an example; there are not any explanation. My Y axis is inverted! How do I fix that? When I play Black Ops 2, it seems that my xbox controller is inverted. Example: if I press up, my character looks down and vice versa. It was not like this before. Does anyone know how to reset the controller back to its original settings? Why would a journal accept my previous paper for publication, but reject latest manuscript due to being "outside of the journal's scope?" I submitted a manuscript last year to an IEEE journal, and the paper was accepted for publication. I recently submitted a new manuscript to the same journal, but, this time, the paper was rejected, and I was told that I should submit to another journal since my paper was not within the journal's scope. The two papers both target similar applications. Furthermore, the second paper uses some work in the first paper, making substantial improvements at solving a much more difficult problem. Based on the reviewer's comments (and my own personal assessment), I do not believe that the work presented in the second paper was "incremental" in nature. Far from it. Two of the three reviewers gave positive reviews. The third reviewer, however, mentioned the "outside of journal's scope" issue and the associate editor and editor-in-chief both sided with the 3rd reviewer, and the paper was stopped dead in its tracks.  I'm scratching my head trying to come to terms with how in the world my first paper could be accepted by this journal, but the second paper focused on the same application space and achieving substantial improvements on a much more difficult problem (backed up with measured results) could be rejected. Any ideas? Whats this white stuff on my board? I'm not an engineer, but my monitor stopped working yesterday (it just wouldn't display anything but still gets power) so I figured I'd like to take it apart and see what went wrong.  At the very least I'd get to see what the inside of a monitor looks like :).  Anyway, I took it apart, and also read around about my issue and it seems the capacitors have gone bad, at least some of them.  However, I also noticed some white elastic stuff all over the board.  Some of them are sticking two capacitors together and to the board, but I also see some from where power socket connects to the board.  My question is, what is the white stuff?  Should I replace all capacitors that have white stuff around it, and should I also replace the power socket part?  Or should I just replace the bulging capacitors and leave it at that?  UPDATE: What are the numbers / symbols to the right of my reputation counter? How to initialize a JavaScript Date to a particular time zone How can I distribute a native executable for a Python program? Elsarticle - Abstract two columns wide I am currently trying to create an article in elsarticle style, twocolumn. The title and text end up in two columns, the abstract however is made two columns wide. Any ideas what I am doing wrong? Obviously I want my abstract to also be only in the first column.  \documentclass[a4paper,10pt,twocolumn,preprint]{elsarticle}  \usepackage{lipsum}  \journal{TexExchange}   \begin{document}     \begin{frontmatter}       \title{Two-column abstract}       \begin{abstract}         \lipsum[1]      \end{abstract}       \begin{keyword}        abstract      \end{keyword}    \end{frontmatter}   \section{Outline}    \lipsum[2-3]  \end{document} A Putnam Integral $\int_2^4 \frac{\sqrt{\ln(9-x)}\,dx}{\sqrt{\ln(9-x)} + \sqrt{\ln(x+3)}}.$ This is a Putnam Problem that I have been trying to solve (on and off) for two years, but I have failed. I am in Calculus BC. This problem comes from the book "Calculus Eighth Edition by Larson, Hostetler, and Edwards". This problem is at the end of the first section of the chapter 8 exercises. Here's the problem:  Evaluate $$\int_2^4 \frac{\sqrt{\ln(9-x)}\,dx}{\sqrt{\ln(9-x)} + \sqrt{\ln(x+3)}}.$$  Please. Any help is very much appreciated. So are solutions. Thank you!  Edit: I like the solution given, but I was interested to see if there is any other way of doing the problem? I'm excited to see the results. "He is king" vs "He is a king." I'm reading a book and encountering the phrase "insert name is king" a lot. I'm wondering, what's the difference between them? When and why should I use "He is king" instead of "He is a king"?   Examples:        Tommen is king now   Yet if neither one is king, still, how could it be Lord Renly?   And he is a king, and you’re just a spy   Everyone else is a king or prince these days      Same with other words:        They elected him president.   They called him a thief. I am playing with LINQ to learn about it, but I can't figure out how to use Distinct when I do not have a simple list (a simple list of integers is pretty easy to do, this is not the question). What I if want to use  on a list of an Object on one or more properties of the object?  Example: If an object is Person, with Property Id. How can I get all Person and use Distinct on them with the property Id of the object?  Person1: Id=1, Name="Test1" Person2: Id=1, Name="Test1" Person3: Id=2, Name="Test2"   How can I get just Person1 and Person3? Is that possible?  If it's not possible with LINQ, what would be the best way to have a list of Person depending on some of its properties in .NET 3.5? "Give him a box that everyone knows what it contains."  Is this correct English? It sounds wrong to me. $Path hijacked by PacletManager? Why is Outlook 2010 Changing my Embedded Spreadsheet to a GIF? Years ago I figured out how to embed a spreadsheet in an Outlook email to automate a task I do regularly.  Whenever I want to send a new quote request I open an old email, tell Outlook I want to resend it, fill in the new values in my embedded spreadsheet and then send it off.  This method worked well for years.  After switching to a new computer however, I have found that when I open the latest emails I have sent, I cannot edit the embedded spreadsheet because Outlook interprets it now as a GIF.  Saved emails that I sent with the old computer however, still work fine - I can still open, edit and resend and Outlook interprets the embedded spreadsheet correctly.  I would like to figure out how to setup Outlook in the new PC correctly so that the embedded spreadsheet is interpreted correctly when the email is reopened. Some sort of security setting, maybe?  Any help anyone could provide would be appreciated.  Edit: I developed the spreadsheet originally in Excel. Then I went into Outlook, created a new email, did Insert->Object->Excel Spreadsheet. At that point I had a blank spreadsheet in my email. Then I copied and pasted the spreadsheet from Excel into the blank spreadsheet in Outlook and it worked perfectly (until this recent problem) Summing the power series $\sum\limits_{n=0}^\infty (-1)^n \frac{x^{2n+1}}{2n+1}\prod\limits_{k=1}^n\frac{2k-1}{2k} $ I'd like to determine the function corresponding to the following power series: $$x + \sum_{n=1}^\infty (-1)^n\frac{1\cdot3\cdot5\cdots(2n-1)}{2\cdot4\cdot6\cdots2n} \frac{x^{2n+1}}{2n+1}, $$ where $|x|&lt;1$. I am curious about the proof of these two integrations. It would be great if you could point me in the right direction : $ \int{e^{ax}\cos({bx})dx}= \dfrac{e^{ax}}{a^{2}+b^{2}}[a\cos(bx)+b\sin(bx)] + C $ &amp; $ \int{e^{ax}\sin({bx})dx}= \dfrac{e^{ax}}{a^{2}+b^{2}}[a\sin(bx)-b\cos(bx)] + C $