list1 = [1, 2, 3, 4]   element = list1[1:][1]    print(element)   Why does it print 3?   How is this evaluated? Does it first take the elements of list1 that are from index 1: then it takes the 1 index of that?
I need a good explanation (references are a plus) on Python's slice notation.   To me, this notation needs a bit of picking up.   It looks extremely powerful, but I haven't quite got my head around it.
Computing matrices of linear transformation under different basis Came across a problem in my textbook and I am having trouble with it, the book provides an answer but no workings. Looking to get an explanation of what is going on  help I prepare for an exam. If we let $T : \mathbb R^2 \to \mathbb R^2$ be a linear transformation. Consdider two bases $V$ and $W$ of the vector space $\mathbb R^2$, where $V=\{v_1,v_2\}$ with $ v_1 =  \begin{bmatrix} -2 \\1   \end{bmatrix}$ and  $ v_2 =  \begin{bmatrix} 1 \\1   \end{bmatrix}$ and where $W = \{w_1,w_2\}$ with  $ w_1 =  \begin{bmatrix} -1 \\4   \end{bmatrix}$ and  $ w_2 =  \begin{bmatrix} 0 \\1   \end{bmatrix}$. Suppose that  $ A =  \begin{bmatrix} 1&amp;2   \\-1 &amp;4    \end{bmatrix}$ is the matrix of $T$ under basis $W$. I need to find the matrix $B$ the matrix of $T$ under basis $V$.  The solution is:   $ B = P^{-1}AP$ = $   \begin{bmatrix} -30&amp;22   \\-48 &amp; 35    \end{bmatrix} $  But I don't know why. On convergence of Bertrand series $\sum\limits_{n=2}^{\infty} \frac{1}{n^{\alpha}\ln^{\beta}(n)}$ where $\alpha, \beta \in \mathbb{R}$ Study the convergence of $$\sum_{n=2}^{\infty}  \frac{1}{n^{\alpha}\ln^{\beta}(n)}$$ where $\alpha, \beta \in  \mathbb{R}$   I have proved that:   This series diverges when $\alpha \leq 0$. This series converges when $\alpha &gt; 1, \beta &gt; 0$ This series diverges when $0 &lt; \alpha &lt; 1, \beta &gt; 0$ This series converges when $\alpha = 1, \beta &gt; 1$      Question: What happens when $\alpha &gt; 0$ and $ \beta &lt; 0$?   There are other questions on MSE which ask about this series, but this question is distinct because   I would like an argument which does not rely on the integral test for series convergence, and this question considers all real $\alpha$ and $\beta$, while other questions ask only about $\alpha, \beta &gt; 0$, where we can apply Cauchy condensation criterion We add negative numbers and zero to natural sequence to make it closed under subtraction, the same thing happens with division (rational numbers) and root of -1 (complex numbers).  Why this trick isn't performed with division by zero? $\lim_{n\to\infty}((\frac94)^n+(1+\frac1n)^{n^2})^{\frac1n}$  Here's what I did:  $\lim_{n\to\infty}((\frac94)^n+(1+\frac1n)^{n^2})^{\frac1n}\\ =(\lim(\frac94)^n+\lim((1+\frac1n)^{n})^n)^{\frac1n}\\ =(\lim(\frac94)^n+\lim e^n)^{\frac1n}\\$  Any hints on how to continue?  PS: no logs/integration/derivation because we haven't covered it. A positive alternative to "smelling" to describe something with a pleasant odor When one hears that something smells, one would generally assume that it smells bad.   Isn't there a word which wouldn't bring to mind the idea of a bad odor? For example, how would you describe pot-pourri (assuming you like the smell of pot-pourri)? If possible, I would like an adjective, or a word that could takes the place of an adjective. Is my processor 64 or 32 bit? How to put a full-width table at the top or bottom of the same two-column page as the reference text? I'm posting today because I would like to reduce white space in a document I'm writing. The content is two-columns but I have floating tables that span across both columns (table*).   At some point, the text ends in the beginning of the first column of a new page. I would like to include my table on this page since it has a lot of free space below the text, but when I insert the table* right after the text, it goes to the top of the next page instead:    Do you know a way of obtaining the desired behavior?  Minimal working example :  \documentclass{article} \usepackage{lipsum}  \begin{document} \twocolumn  \paragraph{} \lipsum[1]  \begin{table*} \centering \begin{tabular}{|c|c|c|c|} \hline Column 1 &amp; Column 2 &amp; Column 3 &amp; Column 4 \\ \hline Column 1 &amp; Column 2 &amp; Column 3 &amp; Column 4 \\ \hline \end{tabular} \end{table*}%   \end{document} In the case of languages with a C-like syntax, we declare the main() method to return an int or float value (or void).  Is it possible to declare a non-void return type from main() in Java?  If not, then why not?  Does this mean that a Java program doesn't return any value to the OS? How to use articles with scientific words, such as mass, force, impulse, field and others? How are articles used with scientific quantities, such as mass, force, impulse, field and others? Evaluate $\lim_{x\rightarrow 0} \frac{\sin (6x)}{\sin(2x)}$ without L'Hopital Limit of a Piecewise Function defined on Rationals and Irrationals Solve the following equation in positive integers $x$ and $y$ How do I use shell variables in an awk script? What is the current state of apple device (iPhone, iPod, etc.) support? How can I deal with "Low on Space" messages on my Android? I keep getting the "Low on Space: Application data space is low. To free up" [the rest is cut off] message.  I've moved every app I can over to the SD card, cleared the cache, compacted my K9 mail cache.  Advanced Task Killer (ouch!) says I have 98M Available Memory  File Manager says I have 223M/748M (29%) free.  That's not so bad -- but I'm stuck in the no-updates scenario. The market downloads won't really start, gmail won't update, etc. I've rebooted several times, and nothing changes. Aaaargh.  What can be done, other than uninstalling everything ? Google AdSense Policy Non Compliant "Site Behaviour: Navigation" Decode escaped Url without using HttpUtility.UrlDecode Is there any function that converts an escaped Url string to its unescaped form? System.Web.HttpUtility.UrlDecode() can do that job but I don't want to add a reference to System.Web.dll. Since my app is not a web application, I don't want to add a dependency for only using a function in an assembly.  UPDATE: Check  about the same issue. This is perhaps a simple question with a simple answer, but I'm stumped as a tikz novice. What would be the best method to add an image (logo) file to the upper left-hand corner of my document?    MWE:  \documentclass[12pt]{article}  \usepackage{lipsum} \usepackage{showframe} %\usepackage{tikz} %\usepackage{graphicx}  \begin{document}  \section*{Lorem Ipsum}  \lipsum[1]  \end{document}   I wish to avoid using fancyhdr to achieve this result. After a few days of operation on my new ec2 build, the following happens:   I log into SSH, everything is fine, I do my coding I return the next day, and log into SSH I cannot type a lower cased e anymore--I get the error ding when I type it I try to ssh from a different computer, same problem I reboot the server, same problem I open nano or vi and e works fine, just not in bash or sh I terminate the server, create a new one, install from scratch, a few days later it happens again   This is baffling! Where do I even start to troubleshoot?  My Local Machine Setup(s):   windows XP or 7 putty (latest) or cygwin/openssh   The EC2 setup   Amazon Linux (default options) node.js iptables forwarding port 80 to node on port 8003 emacs, npm, and openssl-devel no other mods       Output of stty -a while I can't type an e  sh-4.1$ stty -a speed 38400 baud; rows 30; columns 95; line = 0; intr = ^C; quit = ^\; erase = ^?; kill = ^U; eof = ^D; eol = &lt;undef&gt;; eol2 = &lt;undef&gt;; swtch = &lt;undef&gt;; start = ^Q; stop = ^S; susp = ^Z; rprnt = ^R; werase = ^W; lnext = ^V; flush = ^O; min = 1; time = 0; -parenb -parodd cs8 -hupcl -cstopb cread -clocal -crtscts -cdtrdsr -ignbrk -brkint -ignpar -parmrk -inpck -istrip -inlcr -igncr icrnl ixon -ixoff -iuclc -ixany -imaxbel -iutf8 opost -olcuc -ocrnl onlcr -onocr -onlret -ofill -ofdel nl0 cr0 tab0 bs0 vt0 ff0 isig icanon iexten echo echoe echok -echonl -noflsh -xcase -tostop -echoprt echoctl echoke   In case it helps someone else with a similar issue, I created a script (called sub) to convert upper-cased E to lower-cased, then echo the command back. Then I run it in backticks to get an e on the command line::  #!/bin/sh echo ${@//E/e}  &gt; `sub Emacs /Etc/profilE`   UPDATES   This breaks for all users In bash only (csh works fine) In emacs edit mode only   I've created  and hone in the solution. Equidistant points across Bezier curves