Eigenvalue changes in sign when performed row operations.
elementary row operation change the eigenvalue of a matrix
Why is the prospective new kilogram standard a sphere? I can understand the choice of material, silicon 28, but why is it a sphere rather than (say) a cube? Article   I would have thought that a sphere would have been the hardest shape to machine accurately. Converting HTML to plain text in PHP for e-mail How is Dru-Zod/General Zod still alive after this character died? Where is "Regular Solids" option? Following an online tutorial that uses an object named "icosahedron" from Add > Mesh > Regular Solids > Archimedean > Icosahedron. This object is not available in my version of Blender (2.74). Presenter asks me to include an add-on named "Add Mesh: Regular Solids", which again is not listed in my User Preferences dialog. What can I do about it? Mortarboard badges being awarded as a result of bounties after recalc I host am ExpressionEngine based website on a single Amazon EC2 instance in the US East (Virginia) region. I use Ubuntu.    The website allows members to post their content, and displays it for other members and for users who are not logged in.   Goal: I need to begin serving the same website across the globe, equally fast to Hong Kong, New York, and Los Angeles.   I considered two solutions:  1.Setting up three separate EC2 instances for three regions: Virginia, Oregon, and Singapore. Use Amazon Rot53 Geo Location to direct traffic to instances based on the browser's IP address.   Pro: the website will load fast for the region.   Contra: these will be essentially three separate websites. Unless I am mistaken?   Setting up one instance in a region equally remote from all three locations: (Ireliand), and boost the server to the highest performance available.    Pro: It will be the same website for all regions.   Contra: it will cost a lot to make it fast enough.   My challenges:   a) I do not know a way to sync server settings, database, and content between multiple Ubuntu instances in real time. If a knowledgeable person could explain to me how to do that, I would be most grateful.   b) I am not thoroughly familiar with all Amazon AWS resources. Does AWS has a built-in method that would allow me to achieve my goal of serving a single PHP / MySQL based membership website across the globe equally fast in all three chosen locations? Is it possible to call a non-exported function that resides in an exe? If $f:D\to D’$ is analytic and $u: D'\to R$ is harmonic then the composition of $u$ and $f$ is harmonic in $D$ If $f:D\to D’$ is analytic and $u: D'\to R$ is harmonic then the composition of $u$ and $f$ is harmonic in $D$.  How can I show that the above statement is true/false? Can anyone help me? netplan configuration on Ubuntu 17.04 virtual machine I'm running VirtualBox with 2 network adapters: standard NAT (enp0s3) and a Host-only Adapter (enp0s8). I use the NAT to access the internet and the Host-only Adapter to SSH in from my local machine.  The box boots up with both adapters enabled, both have IP addresses, everything looking good.    I can SSH into this box over the host-only adapter, no issues there. But I can't get on the internet with it. However, if I disable the host-only adapter, then I can access the internet (but obviously I can no longer SSH into it over the local tunnel).    And finally, here is my netplan yaml config:  # This file describes the network interfaces available on your system # For more information, see netplan(5). network:   version: 2   renderer: networkd ethernets:   enp0s3:     dhcp4: yes     dhcp6: yes   enp0s8:       dhcp4: no     dhcp6: no     addresses: [192.168.52.101/24]     gateway4: 192.168.52.101   Any ideas? It seems like maybe all my outbound traffic is routing through the host-only adapter somehow.  Edit: attaching the output of ip route list in case it helps.  default via 192.168.52.101 dev enp0s8 proto static default via 10.0.2.2 dev enp0s3 proto dhcp src 10.0.2.15 metric 100 10.0.2.0/24 dev enp0s3 proto kernel scope link src 10.0.2.15 10.0.2.2 dev enp0s3 proto dhcp scope link src 10.0.2.15 metric 100 192.168.52.0/24 dev enp0s8 proto kernel scope link src 192.168.52.101 I am trying to filter items with a stored procedure using like. The column is a varchar(15). The items I am trying to filter have square brackets in the name.  For example:  WC[R]S123456.  If I do a LIKE 'WC[R]S123456' it will not return anything.  I found some information on using the ESCAPE keyword with LIKE but I do not understand how to use it to treat the square brackets as a regular string. Test for the convergence of the sequence $S_n =\frac1n \left(1 + \frac{1}{2} + \frac{1}{3} + \cdots+ \frac{1}{n}\right)$ How to store lots of small text in a SQL Server database? I know that the Naruto movies are outside the timeline in the sense that they don't affect whatever happens after them. However, they must fall somewhere in the Naruto timeline — based on who are in the movies and how the characters look like, etc. For example, if Sasuke isn't in the movie, it should take place after he left. For each of the movies, approximately what timeframe (between episodes/arcs) are they set?  The movies:   Ninja Clash in the Land of Snow Legend of the Stone of Gelel Guardians of the Crescent Moon Kingdom Naruto Shippuden the Movie Bonds The Will of Fire The Lost Tower Blood Prison Road to Ninja The Last - Naruto the Movie Boruto: Naruto The Movie How do a tile with diagonal lines in Photoshop? How does one draw a tile with diagonal lines that can seamlessly tiled with Photoshop? "Delete this answered question?" when the only answer is deleted Looks like there's a small bug in the UI: I posted a question here on meta.SE which ended up being just something dumb I was doing and no use to anyone in the future. At first I posted an answer saying what the dumb thing was, but then I realized that the whole thing had no value, so I deleted the answer, and then deleted the question — whereupon it asked me:  Delete this answered question? We do not recommend deleting questions with answers because doing so deprives future readers of this knowledge. Repeated deletion of answered questions can result in your account being blocked from asking. Are you sure you wish to delete?  (Screenshot below) Probably shouldn't ask (or add to the tally) if the only answers are deleted ones... It seems that a number of the statistical packages that I use wrap these two concepts together. However, I'm wondering if there are different assumptions or data 'formalities' that must be true to use one over the other. A real example would be incredibly useful. How do I show that $x^4-10x^2+1$ is irreducible over $\mathbb{Q}$? Someone says I should use the rational root test, but I don't exactly know how that applies. Thanks for any input. Possible Duplicate:                If in a multiple linear regression (enter method) the general model isn't significant (F>.05) but one of the predictors is significant (β&lt;.05), should I consider it as a significant result? I'm reading Linear Algebra by Hoffman, Kunze where the authors explained that a $n\times n$ matrix $A$ being invertible is equivalent to the fact that $A$ is row-equivalent to $n\times n$ matrix $R$ which is an identity matrix.  In the proof of the theorem, they wrote:     $$R= E_k\ldots E_2E_1 A$$ where $E_1,\ldots,E_k$ are elementary matrices. Each $E_j$ is invertible, and so $$A = E_1^{-1}\ldots E_k^{-1}~R\,. $$  ... Since, $R$ is a (square) row-reduced echelon matrix, $R$ is invertible if and only if $R=I\,.$  [...]   I couldn't get the conclusion, since any row of $R$ can't be zero, it has to be identity matrix $I\,.$ Why is it so?  Isn't there any other row-reduced echelon matrix other than the identity matrix having no zero row and invertible? Why is it so? how does systemd determine service is stopped?