I have a symmetric matrix as shown below  $$\begin{pmatrix} 0&amp;2&amp;1&amp;4&amp;3 \\ 2&amp;0&amp;1&amp;2&amp;1 \\ 1&amp;1&amp;0&amp;3&amp;2 \\4&amp;2&amp;3&amp;0&amp;1 \\ 3&amp;1&amp;2&amp;1&amp;0\end{pmatrix}$$   Does this matrix belong to a particular type?     I am CS student and not familiar with types of matrices. I am researching to know the particular matrix type since I have a huge collection of matrices similar to this one. By knowing the type of matrix, maybe I can go through its properties and work around easier ways to process data efficiently. I am working on a research project in Data Mining. Please help.  P.S.: Only the diagonal elements are zero. Non diagonal elements are positive.
I'm interested in the properties of zero-diagonal symmetric (or hermitian) matrices, also known as hollow symmetric (or hermitian) matrices.   The only thing I can come up with is that it cannot be positive definite (if it's not the zero matrix): The Cholesky decomposition provides for positive definite matrices $A$ the existence of a lower triangular $L$ with $A=LL^*$. However the diagonal of $LL^*$ is the inner product of each of the rows of $L$ with itself. Since the diagonal of $A$ consists of zeros, so $L$ (and thus $A$) must be the zero matrix.  The sorts of questions that interest me are:   which symmetric matrices can be transformed orthogonally into a zero-diagonal matrix? what can we say about the eigen-values of a zero-diagonal symmetric matrix?. any other interesting known properties??
To prove the convergence of the p-series   $$\sum_{n=1}^{\infty} \frac1{n^p}$$  for $p &gt; 1$, one typically appeals to either the Integral Test or the Cauchy Condensation Test.  I am wondering if there is a self-contained proof that this series converges which does not rely on either test.    I suspect that any proof would have to use the ideas behind one of these two tests. Entire function problem: translation If a permanent turns into a(nother) creature, has it entered the battlefield? I was playing a game last night with a guy who was playing a new Simic Gatecrash deck, and he claimed that if he made a land into a creature, it counted as entering the battlefield, thus triggering evolve (or other "enters the battlefield" abilities).  I thought this was incorrect, being that the creature didn't actually enter the battlefield, it was just created.  Which of us was right? The Additional Drivers settings interface is no longer available in Ubuntu 17.10  How can I install proprietary drivers in Ubuntu 17.10?  I need drivers for Wifi &amp; Bluetooth (BCM43142) and Intel Graphics.  The earlier Additional Drivers program showed a package named jockey but it no longer seem to exist in repositories. Help me to solve this problem please..  Let $Y_{(1)}, Y_{(2)}, Y_{(3)}, Y_{(4)}, Y_{(5)}$ denote the order statistics of a random sample of size 5 from a distribution having p.d.f. $f(y) = e^{(-y)}, 0 &lt; y &lt; \infty$, zero elsewhere. Show that $Z_1 = Y_{(2)}$ and $Z_2 = Y_{(4)} − Y_{(2)}$  are independent. Hint: First find the joint p.d.f. of $Y_{(2)}$  and  $Y_{(4)}$. Limit of $\lim_{(x,y)\rightarrow(0,0)}\frac{x^2y^2}{x^3+y^3}$ I want to know whether $\lim_{(x,y)\to (0,0)}\dfrac{x^2y^2}{x^3+y^3}$ exists or not. I tried to approximate to (0,0) from different "paths" and the result was always 0. For example,  $f(x,mx^2) = \dfrac{m^2x^3}{1+m^3x^3}$  But that doesn't show that the limit is 0. I believe there are several ways to prove that $\sum\limits^{\infty}_{n=1}\left(1-\frac{1}{\sqrt{n}}\right)^n$ converges. Can you, please, post yours so that we can learn from you?  HERE IS ONE   Let $n\in\Bbb{N}$ be fixed such that $a_n=\left(1-\frac{1}{\sqrt{n}}\right)^n.$ Then, \begin{align} a_n&amp;=\left(1-\frac{1}{\sqrt{n}}\right)^n \\&amp;=\exp\ln\left(1-\frac{1}{\sqrt{n}}\right)^n\\&amp;=\exp \left[n\ln\left(1-\frac{1}{\sqrt{n}}\right)\right] \\&amp;=\exp\left[ -n\sum^{\infty}_{k=1}\frac{1}{k}\left(\frac{1}{\sqrt{n}}\right)^k\right]\\&amp;=\exp\left[ -n\left(\frac{1}{\sqrt{n}}+\frac{1}{2n}+\sum^{\infty}_{k=3}\frac{1}{k}\left(\frac{1}{\sqrt{n}}\right)^k\right)\right]\\&amp;=\exp \left[-\sqrt{n}-\frac{1}{2}-\sum^{\infty}_{k=3}\frac{n}{k}\left(\frac{1}{\sqrt{n}}\right)^k\right]\\&amp;\equiv\exp \left(-\sqrt{n}\right)\exp \left(-\frac{1}{2}\right)\end{align} Choose $b_n=\exp \left(-\sqrt{n}\right)$, so that  \begin{align} \dfrac{a_n}{b_n}\to\exp \left(-\frac{1}{2}\right).\end{align} Since $b_n \to 0$, there exists $N$ such that for all $n\geq N,$ \begin{align} \exp \left(-\sqrt{n}\right)&lt;\dfrac{1}{n^2}.\end{align} Hence, \begin{align}\sum^{\infty}_{n=N}b_n= \sum^{\infty}_{n=N}\exp \left(-\sqrt{n}\right)\leq \sum^{\infty}_{n=N}\dfrac{1}{n^2}&lt;\infty,\end{align} and so, $\sum^{\infty}_{n=1}b_n&lt;\infty\implies \sum^{\infty}_{n=1}a_n&lt;\infty$ by Limit comparison test. I have a rechargeable vacuum cleaner with NiMH batteries, 1800mAh and 14.4 volts, 12 cells. The charger is 18v 200mA. The batteries have now died.  Can I replace the batteries with 4 cell Li-ion in series?   That will be 14.4 volts, if considered 3.7v each. Of course, I know it will be roughly 4 volts when fully charged.  Li-ion batteries in my mind: 18650, 2500mAh.  Also, can I charge them with the same charger? Is Java "pass-by-reference" or "pass-by-value"? I always thought Java uses pass-by-reference. However, I've seen a couple of blog posts (for example, ) that claim that it isn't (the blog post says that Java uses pass-by-value). I don't think I understand the distinction they're making. What is the explanation? Is irrational times rational always irrational? Is an irrational number times a rational number always irrational?  If the rational number is zero, then the result will be rational. So can we conclude that in general, we can't decide, and it depends on the rational number? A non-trivial, non-negative, function bounded below by its derivative with $f(0)=0$? I did not know what to search to see if this existed elsewhere. But, I could not find it. Here's the question:  Does there exist a continuously differentiable function, $f: [0,1] \rightarrow [0, \infty)$, such that the following hold? (i) $f(0) = 0$ (ii) $f'(x) \le c f(x)$ for all $x$ ($c$ is a fixed constant) (iii) $f \not\equiv 0$  This was a fun problem someone asked me a long time ago. I have always been convinced there is no such function, but I cannot prove it. I have mainly tried using the mean value theorem (in multiple forms), and re-wording the problem in terms of the integral of a continuous function to no avail. I spent some time trying to use (ii), the definition of derivative, and squeeze theorem, but no luck. After much time trying to prove non-existence, I spent a little time trying to find such a function... also with no luck. This problems ability to avoid being solved has since taken away the original fun and replaced it with a twinge of annoyance. To post an image in a question/answer an user requires at least 10 rep points (see ). To be able to upload an image in the chat, the rep requirements is instead 100 rep point (see ).  Is there any reason to that? I am asking because IF the rationale is to provide more protection inside the chat, the protection is easily circumvented by uploading the image via the question editor, and then copying the link to the chat. Basically, the more restrictive requirement fail to reach its goal - assuming that blocking uploads from new users was indeed the target.  I am not proposing to change that (it doesn't seem worthy the effort) but I was curios to know if this is just a refuse caused by successive changes to the system or if there is actually a different rationale to this that I am missing.  [note: I will remove the double Discussion/Support tag as soon as I can focus if the question has a staff answer - support or will prompt a discussion] Adding CSS Reference on Site Page So I have created a Site Page that has the "New Experience" look and I would like to change its style a little. Nothing major, just the height, width, color, etc. However, I can not seem to figure it out.   For example, I tried to change the height of the .pageHeader to a smaller value.   .pageHeader{ height: 150px !important } //for example of CSS in file   Here is a reference image of the page i'm trying to change    I tried adding   &lt;link href="../SiteAssets/file.css" rel="stylesheet" type="text/css"&gt;   to the .aspx page using SharePoint Designer and it didn't work.    I also tried adding   &lt;SharePoint:CssRegistration ID="CssRegistration" Name="SiteAssets/file.css" runat="server" /&gt;   to the .aspx page and it didn't work    I tried to use the "Embed" feature to add the CSS; however, it complains and says,     This embed code doesn't seem to work. We only support iframe based embeds.   Question:   How can I add custom CSS to this type page?  I can't seem to figure it out and I'm not sure exactly why the page will not load the file.  Is this even possible? Books or resources for learning unified view of classical statistics? I did a science PhD doing applied bayesian statistics, and I liked it so much that I decided to shift to statistics.  For the last 2-3 years have been working at a firm that has more of a frequentist focus.  It seems to me that the bayesian approach (at least what I learned) has an underlying theory that was laid out and I could understand.  Now I find this - more classical - field fascinating but I am looking for some resources to get a unified view of the matter.  For example, I am learning and applying anovas, F-tests and chi-squares, thinking about degrees of freedom, etc but part of me is looking for deeper understanding that would make it more than just methods.  Does anyone have any suggestions on books or more resources that provide such a unified, deeper focus? Sound of a next scene starts one moment earlier than video I saw this several times in different movies, but I don't understand what is this supposed to mean. The main idea is when the scene is about to change, for one second or so we still see the picture from the old scene, but the sound is already coming from from the upcoming scene. Why do they do this? What's the purpose of this technique? Parallel universes: are there an infinite amount of universes? Parallel universe: in every universe, you are presented with a different decision. Does that mean there are an infinite amount of parallel universes? I.e., if in one universe I choose to go left, I am then presented with different choices vs if i choose right, and that creates more universes with more decisions to be made.  Or does it mean that in the end of one's life we end up in the same place, meaning that its just one parallel universe that eventually collides with the other. Sending email in .NET through Gmail Show that $\sin(z) = z$ has infinitely many solutions in complex numbers. Little Picard theorem should help, but using big Picard theorem is undesirable. Thanks a lot! My keyboard has no "media" keys; can I control media without them? My USB keyboard does not have "media" keys -- that is, dedicated keys for play, stop, next, prev, volume up/down, etcetera.    For the sake of this question, I would prefer not to install additional software if I can avoid it.  Is it possible to issue some standard key sequence on a generic USB keyboard that emulates these play, stop, etc. multimedia keys?  Like Ctrl+Alt+Shift+F12 or something obscure like that? Is the universe finite or infinite?