How to write blocks of code
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How come the year doesn't show here? If $a_{ij}=\max(i,j)$, calculate the determinant of $A$ What does "--" (double-dash) mean? I have seen -- used in the compgen command.  For example:  compgen -W "foo bar baz" -- b   What is the meaning of the -- in there? Can a package overwrite the original commands in Latex? An example:  Without the amsmath package:   The equation environment numbers the equation automatically. The align environment cannot be executed.   With the amsmath package:   align and equation work seamlessly in numbering equations: I can use equation to write my first two equations, and align to write my third equation, and Latex will still number them correctly.   My questions are:   Is the code for the command equation after loading the amsmath package still the same as it was before loading the package? Moreover, if this is the case, then, in general, can loading different packages cause conflicts? And how do we avoid it? How can I snap a window in a corner with 18.04? Sending & Receiving SMS via WiFi Is there a way to send and receive SMS when a cellular signal is not available, but WiFi is?  I'm often on-site at locations where the building has a strong WiFi (Internet) connection, but a simple cell signal is spotty at best. Heartbleed: What is it and what are options to mitigate it? I am trying to disable the touchscreen on my Asus S200E laptop.  In Ubuntu 16.04, I was able to do so with this:  Section "InputClass"     Identifier "evdev touchscreen catchall"     MatchIsTouchscreen "on"     MatchDevicePath "/dev/input/event*"     Driver "libinput" EndSection   How can this be done on Ubuntu 18.04? Suppose $f$ and $g$ are continuously differentiable functions such that $f(x) = g'(x)$ and $g(x) = f'(x)$ and that any product of $f, f', g$ and $g'$ is commutative for all $x ∈ R$. Show that $ f^2 − g^2 = C $ for some real constant C  I have actually no clue how to solve this, and would be really greatfull for all the help i can get Changing projection of shapefile in QGIS Suppose that $a_1,a_2, \cdots, a_n$ are $n$ different integers. Then $[(x-a_1)(x-a_2) \cdots (x-a_n)]^2 +1$ is irreducible over $\mathbb Q$.   I've no idea why it is true. Thanks very much. How do I find my follower if and when they leave me? Highest quality website screenshot? I have created a  that i would like to add to my portfolio, but i'm having a hard time getting high quality screenshots of the full site. I tried to save the website as PDF, but that was full of errors, other online services cant recreate the images and so on. I've also just tried to take regular screenshots on the mac at put it all together, but it really lost a lot of quality when i scaled it down.  Any good ideas? :) Vector spaces for the irreducible representations of the Lorentz Group EDIT:  The vector space for the $(\frac{1}{2},0)$ Representation is $\mathbb{C}^2$ as mentioned by Qmechanic in the comments to his answer below! The vector spaces for the other representations remain unanswered.  The definition of a representation is a map (a homomorphism) to the space of linear operators over a vector space. My question is: What are the corresponding vector spaces for the   $(0,0)$ Representation $(\frac{1}{2},0)$ Representation  $(0,\frac{1}{2})$ Representation $(\frac{1}{2},0) \oplus (0,\frac{1}{2}) $ Representation $(\frac{1}{2},\frac{1}{2})$ Representation infinite dimensional Representation? Is the .minecraft folder hidden on a Mac? The question is pretty straight forward. I can get the exit code of the previous command by using $?. But what exactly is it?  I don't think it is a variable, because you can't have any special characters in the name of variable other than _.  foo?foo=10   will result in the error: foo?foo=10: command not found  So if it is not a variable, what is it? Are there others like it? Keeping tables/figures close to where they are mentioned Is there any package or a method to force LaTeX to keep floating environments like table and figure closer to where they are declared? Regarding the ellipsoid computed by using the "lifting step" I need your expertise in understanding and hopefully solving the following problem:  Let $C \subset \mathbb{R}^d$, and lets assume that $C$ is not centrally symmetric, thus when computing the $MVEE(C)$ (i.e the minimum volume enclosing ellipsoid), they use the following "lifting step":  $$ C^\prime = \left\lbrace \pm \begin{bmatrix} x\\ 1 \end{bmatrix} \middle| x \in C \right\rbrace,$$ where $C^\prime$ is centrally symmetric.  It is proven that for any $\varepsilon &gt; 0$, $MVEE(C^\prime) \cap \Pi$ is a $(1 + \varepsilon)$-approximation to $MVEE(C) \times \left\lbrace 1 \right\rbrace$, where $\Pi = \left\lbrace x \in \mathbb{R^{d+1}} \middle| x_{d+1} = 1 \right\rbrace$.  Let $G \in \mathbb{d \times d}$ be an invertible matrix, let $ v \in \mathbb{R}^d$ such that the pair $(G,v)$ represents the matrix and the center of $MVEE(C)$ respectively. Let $\hat{G} \in \mathbb{R}^{(d + 1) \times (d + 1)}$ be an invertible matrix such that the pair $(\hat{G},\overset{\to}{0})$ represents the matrix and center of $MVEE(C^\prime)$ respectively.  Then, $\forall x \in MVEE(C)$ $$ \left| \left| \left[ x , 1 \right] \hat{G} \begin{bmatrix} x\\1 \end{bmatrix} \right| \right|_2 = (1 + \varepsilon) \cdot \left| \left| (x - v) G (x - v)^T \right| \right|_2 .$$  Regarding $x \not\in MVEE(C) $, then it is easy to see that the above term is not satisfied and moreover the right term is bigger or equal to the left term.  What I need to know is whether it possible the bound the right term by the left term (maybe because $MVEE(C) \times \left\lbrace 1 \right\rbrace \subseteq MVEE(C^\prime)$), i.e. $$ poly(d) \cdot \left| \left| \left[ x , 1 \right] \hat{G} \begin{bmatrix} x\\1 \end{bmatrix} \right| \right|_2 \geq (1 + \varepsilon) \cdot \left| \left| (x - v) G (x - v)^T \right| \right|_2 \ ?$$  Please Do correct if I am wrong and thanks in advance. Example of $\deg(fg)<\deg(f)+\deg(g)$ Find the sum of $\sum \limits_{n=1}^{\infty} \frac{2^{-n}(n+3)}{(n+1)(n+2)}$