How to write a matrix like this    I tryed this   $$ \begin{pmatrix} J_0 &amp; O &amp;\cdots\\ 0&amp; J_{n+1} &amp; 0\cdots \end{pmatrix} $$   I don't know how to do
I am struggling to create the matrix in the picture attached using Latex. I have tried using commands like \hline but the matrix ends up looking messy as the line goes all the way across.    Edit: To clarify, I am looking for each block to have a square outline.
ActionBarSherlock + Google Maps API v2 Duplicate Id What Wording Did Witches and Wizards in Other Cultures Use for Spells? What are the different widely used RAID levels and when should I consider them? This is a  about RAID levels.    What are:   the RAID levels typically used (including the RAID-Z family)?  deployments are they commonly found in? benefits and pitfalls of each? Profile changes in Q&A are not pushed to Area 51 I just noticed that the info text on  is an older version of the text in .  I found  from April 2016 where Adam Lear says:     Area 51 is a separate codebase. It's also heavily outdated. Currently we can push a profile update from Q&amp;A to Area 51, but not the other way around   I think the pushing isn't working anymore. I just updated my text on SO again and it was changed in all my accounts, except Area 51. I have ran into some issues when it went down to install Steam on Debian. The console as well as Apper comes up with missing dependencies  and the package isn't going to install. Image, pre-image, and injection proof verification Just wanted to verify this proof was correct. Trying to make sure I have a handle on these subjects before the exam. Any style comments also more than welcome.    Statement: Let $f : A \mapsto B$ be a function. $f$ is injective if and only if for all $X \subseteq A$, $f^{-1}(f(X)) \subseteq X$.  Proof:  $\Rightarrow$ Suppose that $f$ is injective. Let $X \subseteq A$, and let $x \in X$. Since $f$ is injective, $f^{-1}(f(X)) = \{x\} \in X$, so $f^{-1}(f(X)) \subseteq X$.   $\Leftarrow$ Suppose that for all $X \subseteq A$, $f^{-1}(f(X)) \subseteq X$. Let $a_1, a_2 \in A$ and $X = \{a_1\}$. Suppose $f(a_1) = f(a_2)$. If $a_1 \neq a_2$, then $f^{-1}(f(X)) = \{a_1, a_2\} \not \subseteq X$, a contradiction. Thus $a_1 = a_2$, so $f$ is injective. Where To start Learning With Salesforce Development Related:   I have put a bit of commentary enumerating my confusions in parentheses  I read in Black Holes and Time Warps (Kip Thorne), that quasars can generate their jets from four different processes. These all involved the accretion disk, but there was one which doesn't make quite as much sense. It was called the Blandford-Znajek process, and it involved magnetic field lines carrying current.  The process was visualized in two ways. A black hole, with magnetic field lines, is spinning. In the first visualisation (viewpoint actually), the magnetic field lines 'spin' along with the black hole, and nearby plasma is anchored onto the field lines by electrical forces (where did the electrical fields come from?). The plasma can slide along the field lines but not across them (why?).  Since the field lines are spinning, centrifugal forces will fling them up and down the field lines, forming jets.  The other viewpoint is this, and it makes even less sense (to me that is, I haven't had a formal education in GR): The magnetic fields and the swirl of space generate a voltage difference across the field lines (Why? How?). The voltage carries current across the magnetic field lines (why are the field lines behaving like wires?). This current travels across plasma, which accelerates it, creating the jets.  Now the main thing that doesn't make sense, is that magnetic field lines are behaving like wires. Why would they? I suspect the answer lies hidden somewhere in the equivalence of EM waves in different frames, but I can't think up any convincing argument from that side.  If the answer involves GR equations, you don't need to solve it here (wouldn't make sense to me), but if you have to, just refer to the equation and what you did to it, along with the final result. Thanks! Proving Eigenvalue squared is Eigenvalue of $A^2$ The question is: Prove that if $\lambda$ is an eigenvalue of a matrix A with corresponding eigenvector x, then $\lambda^2$ is an eigenvalue of $A^2$ with corresponding eigenvector x.  I assume I need to start with the equation $Ax=\lambda x$ and end up with $A^2 x=\lambda^2 x$ but between those I am kind of lost. I have manipulated the equations several different ways and just can't seem to end up where I need to be. Help would be greatly appreciated as I believe this will be on a test tomorrow. How do I install additional drivers? I've just installed Ubuntu and I need either video, wireless, or some sort of other manufacturer (non-opensource) driver. How can I run the tool that will fetch all of these for me? I'd like graphical instructions.  Related: Is it OK to leave "What have you tried?" comments? Using subcaption package but subfigures end up stacked rather than side by side I'm trying to put two jpegs side by side using the subcaption package, but the images are consistently stacking on top of each other rather than side by side. All the solutions I've found simply state that the pictures have to be small enough to actually be side by side but I've tried making them smaller, too small even and they stay stacked. My code looks like this:  \begin{figure}[H] \centering \begin{subfigure}{0.5\textwidth} \centering     \includegraphics[width=0.3\linewidth]{inclusion.jpg}     \caption{inclusions}     \label{fig:inclu} \end{subfigure}  \begin{subfigure}{0.5\textwidth} \centering     \includegraphics[width=0.3\linewidth]{deform}     \caption{grain deformation}     \label{fig:deform} \end{subfigure} \caption{filler text} \label{fig:manmade} \end{figure}   Help would be greatly appreciated. This is something I've been curious about since starting this whole 'meta' thing a couple years back.     Let's say a user posts a feature request.   Under what circumstances is the feature-request read by staff? If staff decline to do anything (I'd guess it's some sort of triage), under what circumstances is the feature-request reevaluated by staff?     Let's say a user posts a bug.    Under what circumstances is the bug tested? What generally determines whether a verified bug is actionable? (And/or what are the criterion for deciding what to do?)     For both of the above, would it be possible to see a general-but-relatively-detailed flow for what happens to these questions? Why do extract recipes call for a late addition of the bulk of the extract? My recipe calls for a pound of DME at the beginning of the boil and 6 pounds at 15 minutes to go.  What's the point of that? SFDC DKIM Setup - Production or Sandbox? Cannot figure out this via SFDC documentation. Need someone who have setup this before to advise.  Basically we want to enable DKIM for our SFDC org. In testing Sandbox and production, the from email address is using the same email domain. For example, "test@abc.com" for sandbox and "contact@abc.com" in production.   Question: shall we setup DKIM in both sandbox and production or just need to setup in production since sandbox and production are actually using the same domain "abc.com"? today I installed Ubuntu 64-bit on a netbook. When the netbook boots this, error report appeared. I think there is a problem with the partitions.  Gave up waiting for root device. Common problems:   — Boot args (cat /proc/cmdline)     — Check rootdelay= (did the system wait long enough?)     — Check root= (did the system wait for the right device?)   — Missing modules (cat /proc/modules; ls /dev) ALERT! /dev/mapper/ubuntu--vg-root does not exist. Dropping to a shell!   BusyBox v.1.21.1 (Ubuntu 1:1.21.1-1ubuntu1) built-in shell (ash)    Enter 'help' for list of built-in commands.    (initramfs)   Output of lsblk as requested:  $ lsblk NAME   MAJ:MIN RM   SIZE RO TYPE MOUNTPOINT sda      8:0    0 232.9G  0 disk  ├─sda1   8:1    0   231G  0 part  ├─sda2   8:2    0     1K  0 part  └─sda5   8:5    0     2G  0 part [SWAP] sr0     11:0    1   1.2G  0 rom  /cdrom loop0    7:0    0   1.1G  1 loop /rofs How would I prove there is no smallest positive rational number? what is the best method to prove this statement? Measure the size of a PostgreSQL table row I have a PostgreSQL table. select * is very slow whereas select id is nice and quick. I think it may be that the size of the row is very large and it's taking a while to transport, or it may be some other factor. I need all of the fields (or nearly all of them), so selecting just a subset isn't a quick fix. Selecting the fields that I want is still slow. Here's my table schema minus the names: integer                  | not null default nextval('core_page_id_seq'::regclass) character varying(255)   | not null character varying(64)    | not null text                     | default '{}'::text character varying(255)   |  integer                  | not null default 0 text                     | default '{}'::text text                     |  timestamp with time zone |  integer                  |  timestamp with time zone |  integer                  |   The size of the text field may be any size. But still, no more than a few kilobytes in the worst case. Questions  Is there anything about this that screams 'crazy inefficient'? Is there a way to measure page size at the Postgres command-line to help me debug this? Can the JVM recover from an OutOfMemoryError without a restart Vote for Tag Synonyms Directly on the Page Before:  After:   The pros:  Speeds up the tag synonym voting process. Easier to locate (as opposed to navigating to each individual tag wiki page). Encourages users to vote on more than one at a time.  The cons:  Serial up/downvoting. But this really isn't even an issue because, (1) only experienced users can vote on tag synonyms, and (2) more than one vote is required to approve a tag synonym, so the occasional serial up/downvoter won't significantly impact the overall process.