I am referring to Tom Minka's . I don't have the book by Magnus &amp; Neudecker so I can't refer to the details of the theory. Regarding rules (6): $d(XY) = (dX)Y + X(dY)$ and (12): $dX^*=(dX)^*$, I am not clear how to apply them. My notation used is numerator layout, i.e. $\dfrac{dx}{dx} = I$ Question 1. $f(x)=x^Tx$ , $\dfrac{df}{dx}=2x^T$ However, if I use $\dfrac{df}{dx}= x^T\dfrac{dx}{dx} + \dfrac{dx^T}{dx}x$, firstly, $\dfrac{dx^T}{dx}$ is $1^T$? Second, according to rule (12), $\dfrac{dx^T}{dx} = (\dfrac{dx}{dx})^T = I^T = I $? Question 2. $f(x) = x^TAx$ $\dfrac{df}{dx}=x^T\dfrac{dAx}{dx}+ \dfrac{dx^T}{dx}(Ax) = x^TA + ???$ $???$ is supposed to be $x^TA^T$, however, it seems to me no matter $\dfrac{dx^T}{dx}$ equals $1^T$ or $I$ it does not give the expected result.
It's stated that the gradient of:  $$\frac{1}{2}x^TAx - b^Tx +c$$  is   $$\frac{1}{2}A^Tx + \frac{1}{2}Ax - b$$  How do you grind out this equation? Or specifically, how do you get from $x^TAx$ to $A^Tx + Ax$?
Show all inbox items (notifications) in app The SE app currently only shows some inbox items:   Answers Comments Chats   When I see those I assume I'm all caught up, but it turns out there are more on the web which aren't displayed in the app:   Bounty expiration Elections Edits on your own posts Maybe others?   I was about to tag this  but realized it's probably intentional.  I imagine the reason for not showing them is because they're not something you can act on from within the app. Bounties can't be offered or awarded1 and elections can't be voted on.  But then again chats can't be replied to either. Badge descriptions can't be viewed (on the Achievements side). Selecting those launches the browser. Why then shouldn't bounties or elections launch the browser too? Hiding them just means I'll miss it if I haven't visited in browser recently.  1 Though accepting answers does award the bounty phpmyadmin doesn't connection with true data What's the deepest reason why QCD bound states have integer charge? How to obtain the sum of the following series? $\sum_{n=1}^\infty{\frac{n^2}{2^n}}$ What are the most widely used C++ vector/matrix math/linear algebra libraries, and their cost and benefit tradeoffs? Using the expression "the same" for a previously mentioned item Representation of electromagnetic wave? In Representation of electromagnetic waves we show both electric and magnetic fields perpendicular to each other and having zero magnitude at one point and maximum at other point. This representation and understanding of EM waves violating law of conservation of energy... Splitting pieces of a mesh into a new object How to enable bullet points when using the presento beamer theme? I have the problem that when I use an itemize list and the , there are no bullet points.  Here is a minimal working example (requires the  not available on CTAN to be downloaded first):  \documentclass{beamer} \usepackage{config/presento} \begin{document} \begin{frame} \begin{itemize} \item ... \item ... \item ... \end{itemize} \end{frame} \end{document}     How to fix this problem? The difference between two periodic functions converges to zero, is this two functions identical? If $f(x)$ and $g(x)$ are two periodic functions, that is, $f(x+T_1)=f(x)$ and $g(x+T_2)=g(x)$ for every $x \in \Bbb R$. Now that $\displaystyle\lim_{x\to\infty}(f(x)-g(x))=0$.  Conjecture: $f(x) \equiv g(x)$. How to change desktop background from command line in Unity? I have a script that updates my desktop background every day with the NASA APOD. Since upgrading to 11.10, that script stopped working, presumably because I'm using gconftool-2 to actually update the desktop background. Is there a new way to do this under Unity? Returning from Dual-boot to just Windows I installed Ubuntu sometime back along side Vista, but later found that I rarely (if ever) use Ubuntu. How easy is it to return my computer to its initial state of having only one OS, and freeing up the hard-drive space used by the Ubuntu install? Why are my JavaScript objects equal to Proxy {} What is the easiest way to swap occurrences of two strings in Vim? How to escape a single quote? This works fine:  sed -i 's#    @driver.find_element(:xpath, "//a\[contains(@href,##' temp_spec.rb   against a source of  @driver.find_element(:xpath, "//a[contains(@href,'change_district')]").click   I am just left with:  'change_district')]").click`   but when I try to add a single quote at the end it fails:  sed -i 's#    @driver.find_element(:xpath, "//a\[contains(@href,\'##' temp_spec.rb  syntax error near unexpected token `('   I am using \' to escape the single quote.  Note that I am using a # as a delimiter instead of the normal / delimiter as there are /'s in the text. So I'm at that step where I am finally ready to Render my first big project. Aaaaaand it's been stuck on the first 4 tiles for the last 2 hours?   I am using a MacBook Pro Processor: 2.5 GHz Intel Core i5 Memory: 4 GB 1600 MHz DDR3 Graphics: intel HD Graphics 4000 1024 MB  (I include these because I have no idea what affects a computers ability to render but I assume it's one of them, most liekly the graphics card).  So anyways here are the pictures, as you can see I played with changing the resolution, the sample size and the max steps to see if I got different results but it just keeps getting stuck at those 1st four tiles. I've rendered a few other small projects successfully but this was my first time changing some values. I assume i've managed to accidentally change the wrong values and thats causing some conflict thats either stopping the render itself or is making it just too much for my computer.  My goal was the render this particular picture at a good enough resolution and clarity that it could then be made into a poster. So i wanted the resolution to be good and the sampling to be high.       Since writing this there has been no change to any of the numbers at the top of the render result (the time left, etc) The runtime arguments are as follows: $1 is the path to the file containing the list of files $2 is the path to the directory containing the files What I want to do is check that each file listed in $1 exists in the $2 directory  I'm thinking something like:  for f in 'cat $1' do if (FILEEXISTSIN$2DIRECTORY) then echo '$f exists in $2' else echo '$f is missing in $2' sleep 5 exit fi done   As you can see, I want it so that if any of the files listed in $1 don't exist in the directory $2, the script states this then closes. The only part I can't get my head around is the (FILEEXISTSIN$2DIRECTORY) part. I know that you can do [ -e $f ] but I don't know how you can make sure its checking that it exists in the $2 directory. pc ram memory 2x1GB or 1x2GB I don't know if it's the right place to ask but can somebody advise me for buying a ram memory for my computer.  I have a Dell Vostro 200 with 1GB of RAM and 667MHz. (2 x 512MB)  I want to buy raise the amount of RAM but I'm confused whether to buy 1 x 2GB or 2 x 1GB  I know it's the same for the available amount of memory but is ther a difference maybe in the clock speed so that 2 x 667MHz will be better than 1 x 667MHz. or maybe accessing one single memory slot will be faster and better than accessing two slots.  Please anyone helps. Whenever light rays are entering a denser medium they bend towards the normal.  Why do rays choose the path towards the normal? Why cannot they choose the path away form the normal? The Challenge  I have been trying to write a filter that applies (prepends a string) to (a) post titles of a certain post type and (b) to that same post type WordPress admin backend for use by an auto social sharing plugin.  I've gotten really close.  I've achieved: 1.  prepending only to custom post_type post titles 2.  prepending to custom_post type titles AND all nav menu items 3.  prepending to ALL titles (post, page, nav menu, and backend auto-sharing plugin)  The final, 3rd attempt got me very hopeful, but yet still, no matter the function, conditional statement, or combination I use, I can't get custom_post title AND backend social sharing plugin, but not nav menu items.  My Code - what I've tried  I've tried different conditionals, like is_admin() and !is_nav_menu with all nav menu IDs.  I've also tried comparing the ID of the post to the ID of the menu.  Finally, I've also tried adding the filter only to loop_start and that seems promising if combined with other statements.  I will clean up my code for your review but I leave it this way for now in hopes it helps to see what I've tried and maybe where I went wrong with any of those methods.  // , $id = NULL function append_album_review_to_title( $title ) {     global $post;     global $dont_apply_title_filter;     $text = 'Album Review: ';     $prepended_title = $text . $title; /*     $nav_menus_obj = wp_get_nav_menus();     $nav_menu_ids = '';     foreach( $nav_menus_obj as $nav_menu ) {         $nav_menu_ids .= $nav_menu-&gt;term_id . ',';     }     rtrim($nav_menu_ids, ','); */ //  if ( get_post_type( $post-&gt;ID ) == 'album_review' &amp;&amp; in_the_loop() ){ //  if ( get_post_type( $post-&gt;ID ) == 'album_review' &amp;&amp; $id == get_the_ID() ){ //  if ( !is_nav_menu( '32057,32058,35135,32054,32056' ) ) { //  if ( get_post_type( $post-&gt;ID ) == 'album_review' &amp;&amp; is_nav_menu( $id ) ) {     if ( get_post_type( $post-&gt;ID ) == 'album_review' &amp;&amp; !$dont_apply_title_filter ) {         //print_r( $nav_menu_ids );         //print_r( is_nav_menu( $nav_menu_ids ) );         return $prepended_title; /*     } elseif ( get_post_type( $post-&gt;ID ) == 'album_review'  ) {         return $title; */     } else {         return $title;     }; } add_filter('the_title', 'append_album_review_to_title'); //add_action('save_post', 'custom_post_type_title', 100); /* function set_custom_title() {     add_filter( 'the_title', 'append_album_review_to_title', 10, 2 ); } add_action( 'loop_start', 'set_custom_title' ); */