I want to start learning Linear Algebra, I have no background about this subject except high school mathematics that doesn't includes complex number and matrices. I found the following books: Introduction to Linear Algebra by Gilbert Strang and Linear Algebra Done Right and I can't decide which one to choose (if you know a better book, I would like to know).  I also would like to know if there is a practice book or a website with exercises that includes solutions.
I'm starting a very long quest to learn about math, so that I can program games. I'm mostly a corporate developer, and it's somewhat boring and non exciting. When I began my career, I chose it because I wanted to create games.  I'm told that Linear Algebra is the best place to start. Where should I go?
A matrix and its transpose have the same set of eigenvalues/other version: $A$ and $A^T$ have the same spectrum Let $ \sigma(A)$ be the set of all eigenvalues of $A$. Show that $ \sigma(A) = \sigma\left(A^T\right)$ where $A^T$ is the transpose matrix of $A$. Adding my launcher to the Unity Launcher automatically. How? How do I clear command prompts in minecraft? How do websites block selecting text and how do I unblock that? There's a website () that somehow blocks selecting text. Also it blocks Ctrl+A to select everything, there is also no “Copy” in the popup menu.  What I have tried:  Some sites use JavaScript to block selection. So I disabled all JavaScript sources in no-script addon in Firefox. I tried the same site in Google Chrome with the Script Safe addon. Made sure that everything is blocked, still can’t select text. Mousepointer remains an arrow and not a text cursor also on the whole site.  Used about:config to disable JavaScript completely in Firefox. Still no effect.  I read that some sites use DIVs with the style display:block so I used Inspect to examine the styles of the site. There is not one mention of "block" on the whole website, not in embedded CSS nor in object style=-attributes.  The text is not an image or flash or some HTML5 canvas ect. Everything is within DIV and P tags but no style was found that might block the text selection.  How can the website still block any selection of text? Not to mention why browsers support such behaviours at all. I just want to use a selected word or sentence and want to search google for it using right mouse click. It’s pretty annoying when a website does such things and forces me to type technical terms and names into google by hand. It disturbs my workflow. Hardware Enablement Stack (HWE) out of support Prove that $\sin x+2x\ge\frac{3x(x+1)}{\pi}$ for all $x\in [0,\frac{\pi}{2}]$ How do I execute the following shell command using the Python  module?  echo "input data" | awk -f script.awk | sort &gt; outfile.txt   The input data will come from a string, so I don't actually need echo.  I've got this far, can anyone explain how I get it to pipe through sort too?  p_awk = subprocess.Popen(["awk","-f","script.awk"],                           stdin=subprocess.PIPE,                           stdout=file("outfile.txt", "w")) p_awk.communicate( "input data" )   UPDATE:  Note that while the accepted answer below doesn't actually answer the question as asked, I believe S.Lott is right and it's better to avoid having to solve that problem in the first place! Uninstalling Homebrew messed up git I uninstalled Homebrew using .  After running the above commands, I can't find .bashrc and .bash_profle. All files are gone from Documents , Desktop and Downloads :'(  When I do git status on /Users/ava it shows:  # On branch master # Untracked files: #   (use "git add &lt;file&gt;..." to include in what will be committed)  ... all the files which are in /Users/ava   history   113  cd `brew --prefix`   114  rm -rf Cellar   115  brew prune   116  rm `git ls-files`   117  rm -r Library/Homebrew Library/Aliases Library/Formula Library/Contributions   118  rm -rf .git   119  rm -rf ~/Library/Caches/Homebrew   120  sudo chown -R $USER:admin /usr/local   121  ruby -e "$(curl -fsSL https://raw.github.com/mxcl/homebrew/go)"   122  brew doctor   What just happened? How old is Chewbacca, anyway? Do Wookiees get gray fur when they are old? Maximal inequality for a sequence of partial sums of independent random variables Let $X_n$, $n=1,2,3,...$ be a sequence of independent (not necessarily identically distributed) random variables, let $S_n=\sum_{i=1}^nX_i$. Prove the following maximal inequality: For all $t&gt;0$,$$\mathbb{P}\left(\max_{1\leq i\leq n}|S_i|\geq t \right)\leq 3\max_{1\leq i\leq n}\mathbb{P}\left(|S_i|\geq\frac{t}{3} \right)$$ Delete all lines in Notepad++ except lines containing a word I need? Equivalent Definitions of the Operator Norm I am looking at some code and it has this statement:    ~ConnectionManager() {     Dispose(false); }   The class implements the IDisposable interface, but I do not know if that is part of that the tilde(~) is used for. How could I place objects (buildings) on a flat surface in the BGE? I'm working on an  in BGE, and I am not sure how I could make it so you can place buildings on flat surfaces (or unless there is an easier way). I would love to know how to place buildings when you click a certain button to place it.  I don't really need anything fancy like price and stuff like that yet. I really have no idea if  is required to do this. How do I install Java? How do I install Java, including in my browser, so websites with Java work? Given $a>b>2$ both positive integers, which of $a^b$ and $b^a$ is larger? Given $a&gt;b&gt;2$ both positive integers, which of $a^b$ and $b^a$ is larger?  I tried an induction approach. First I showed that if $b=3$ then any $a \geq4$ satisfied $a^b&lt;b^a$.  Then using that as my base case I tried to show that given any pair of positive integers $a,b$ satisfying $a&gt;b&gt;2$ and $a^b&lt;b^a$, then $(a+1)^{b+1}&lt;(b+1)^{a+1}$ - but that is where I got stuck.  Any help would be appreciated. How do I beat the Reaper on Rannoch? I'm having trouble with the last of the Rannoch missions, where Shep wakes up and takes on a Reaper.   Shepard has a targeting laser which will call in an orbital strike with the combined might of the Quarian Migrant Fleet, but there's two major problems standing between the commander and victory.   The Targeting Laser takes a while to power up. The Reaper is trying to kill you.   I can consistently avoid the Reaper's attacks for the first volley, but each time you hit it, the Reaper moves forwards, giving you less time to dodge future assaults. Is there some key to avoiding the Reaper's attacks? Strafing doesn't seem to be enough. I am studying the function and characteristic of an op-amp to build a line-following robot with the schematics below. However, in many tutorials, the way to differentiate an inverting and non-inverting op-amp is by looking at the connection to ground via the inverting or non-inverting terminal.  However, in the schematics, the op-amp is considered to have connections to ground, thus in this case, how do I differentiate it then?  I may have understood the whole concept wrongly. Pls help!    EDIT: Please ignore the switch as it may have been drawn wrongly by the supplier. How to adjust font features in LuaTeX? As of version 2.7 of luaotfload the support for font feature files (.fea) .  On the  Hans showed how to make font substitution work through Lua.  More examples are available in the latest ConTeXt distribution (, , , , , , )  In the past I have been using font feature files to adjust the kerning of fonts on-the-fly.  From Hans' example it is not clear to me how to adjust kerning in the new syntax.  The below example does not work as intended.  \documentclass{article} \usepackage{fontspec} \directlua{ fonts.handlers.otf.addfeature {     name = "kern",     {         type = "pair",         data = {             [0x0041] = { [0x0056] = { false, { -200, 0, 0, 0 } } },         }     } } } \setmainfont{Latin Modern Roman} \begin{document} AV \end{document}   Can we have a comprehensive guide on how to adjust font features with LuaTeX with the fonts.handlers technique?    Related questions:  (These involve hooking into the luaotfload.patch_font callback) How do I get a gnome-terminal window to open from a crontab?  I have tried this:      * * * * * /usr/bin/gnome-terminal       * * * * * source /home/user_name/.bashrc ; /usr/bin/gnome-terminal      * * * * * source /home/user_name/.profile ; /usr/bin/gnome-terminal      * * * * * source /home/user_name/.bashrc ; /home/user_name/bin/opengnometerminal.sh   None of these seem to work.