how do i do the derivative of frobenius norm I am trying to do matrix factorization.  $ \frac{1}{2} \vert\vert X - WZ ^T \vert\vert ^2_F $  How do I find the derivative wrt W ?  I am just told that it is $  W^T = (Z^TZ + \lambda I_K)^{-1}Z^TX^T $  I come from a lousy school please help show me the way.
How To quickly do derivatives with respect to matrices Whats a quick way to work the below (and problems similar) out?   For me to take this derivative it involves a lot of time and boring calculation, there has to be a better way.    This is taken from the solutions to Chris Bishop's Pattern Recognition and Machine learning:
How do I install Adobe Flash player? Julian day of the year in Java I have a question that bothers me after reading a part of the big book of rules :).  It's about the rule 717, illegal actions.     717.1. If a player realizes that he or she can’t legally take an action after starting to do so, the entire action is reversed and any payments already made are canceled. No abilities trigger and no effects apply as a result of an undone action. If the action was casting a spell, the spell returns to the zone it came from. The player may also reverse any legal mana abilities activated while making the illegal play, unless mana from them or from any triggered mana abilities they triggered was spent on another mana ability that wasn’t reversed. Players may not reverse actions that moved cards to a library, moved cards from a library to any zone other than the stack, or caused a library to be shuffled.   For example, player A plays a .     As an additional cost to cast Goblin Grenade, sacrifice a Goblin.   Goblin Grenade deals 5 damage to target creature or player.   It goes on the stack. Player B gains priority and casts a  on the only goblin of Player A.     Destroy target nonartifact, nonblack creature. It can't be regenerated.   The terror goes on the stack. Then both players agree to resolve the stack. The terror kills the last goblin standing and then the Goblin Grenade can't be cast because of the additional cost which can't be paid. So in my opinion that leaves two possibilities:   The Goblin Grenade returns to the zone it was previously from (the hand of Player A) The Goblin Grenade becomes illegal and gets countered, so it goes to the graveyard   Based on rule 717 I think it goes back to the hand but I'm not quite sure. :) Is it possible to test apex that relies on field history tracking? I have some code that relies on field history tracking by querying the History for a custom object. This works fine, but it appears that the history records aren't created during the test so none of my tests will pass. True for every formula. For a formula $ \gamma = r \iff (p_1 \vee p_2) $ there is true that: $\rho \models \gamma \iff \rho(r) = \max(\rho(p_1), \rho(p_2))$  Is it a true for every formula r? How does an accelerating charge radiate electromagnetic waves? The statement is:     In a commutative ring with 1, every proper ideal is contained in a maximal ideal.   and we prove it using Zorn's lemma, that is, $I$ is an ideal, $P=\{I\subset  A\mid A\text{ is an ideal}\} $, then by set inclusion, every totally ordered subset has a bound, then $P$ has a maximal element $M$.  My question is why $M$ must contain $I$? Javascript determine if such object property exists based on a string Prove that if a function $f$ has a jump at an interior point of the interval $[a,b]$ then it cannot be the derivative of any function. Prove that if a function $f$ has a jump at an interior point of the interval $[a,b]$ then it cannot be the derivative of any function.  I know that for $f$ is differentiable in $(a,b)$ and that it has one-sided derivative $f_+' (a)≠f_-' (b)$ at the endpoints. If $C$ is a real number between $f_+' (a)$  and $f_-' (b)$, then there exists $c∈(a,b)$ such that $f' (c)=C $. How can I use this to prove the above? What is the use for non-inverting input resistance in a negative feedback opamp? Here in the Figure R5=50K. This resistor value is not in the equations to obtain output voltage, and in many tutorials non-inverting input is directly grounded without a resistor. What might be the reason to use it here? Explicitly finding the sum of $\arctan(1/(n^2+n+1))$ How do I reset proxy in terminal to automatic if not connected via proxy I tried to reset proxy of the terminal by some commands but it doesn't happen and automatically switches back to this proxy 172.16.0.16 (which apparently was my college proxy).   I checked in my system settings.I don't understand why this is recurring. Please be comprehensive.Also I further would like to know how to bypass proxy server since I couldn't access any of the ubuntu repositories as they were blocked in my college's proxy settings as is Ubuntu's homepage.  Thanks for your time.    For sudo ls /etc/apt/apt.conf.d/        It displays a different set of options where proxy is not listed.I am on 12.10,if this should help any.I put a snap of the terminal after the above command has been entered. How to select JSF components using jQuery? I'm looking to get that from a graph. but problem is that graph is in image form. Now I want to extract data in excel from that graph. how can i do it? I'm using office 2003. What is the current state of apple device (iPhone, iPod, etc.) support? Floquet and Bloch's theorems : connection? It is often stated that  and  are equivalent, even the Bloch's theorem is often referred as Floquet-Bloch theorem.  However, it seems quite confusing to me since the former involves a second order differential equation (Schroedinger equation with a periodic potential) while the latter is defined for a first order one.  Can someone clarify this to me? Also it would be nice if I can get references that connect the two. Approximating a $\sigma$-algebra by a generating algebra Theorem. Let $(X,\mathcal B,\mu)$ a finite measure space, where $\mu$ is a positive measure. Let $\mathcal A\subset \mathcal B$ an algebra generating $\cal B$. Then for all $B\in\cal B$ and $\varepsilon&gt;0$, we can find $A\in\cal A$ such that $$\mu(A\Delta B)=\mu(A\cup B)-\mu(A\cap B)&lt;\varepsilon.$$  I don't think there is a proof in this site. It's a useful result for several reasons:  We know what the algebra generated by a collection of sets is, but not what the generated $\sigma$-algebra is. The map $\rho\colon \cal B\times\cal B\to \Bbb R_+$, $\rho(A,A')=\mu(A\Delta A')$ gives a pseudo-metric on $\cal B$. This makes a link between generating for an algebra and dense for the pseudo-metric. We say that a $\sigma$-algebra is separable if it's generated by a countable class of sets. In this case, the algebra generated by this class is countable. An with the mentioned result, we can show that $L^p(\mu)$ is separable for $1\leq p&lt;\infty$, which makes a link between the two notions. In ergodic theory, we have to test mixing conditions only an a generating algebra, not on all the $\sigma$-algebra. I want to write a function in Python that returns different fixed values based on the value of an input index.    In other languages I would use a switch or case statement, but Python does not appear to have a switch statement.  What are the recommended Python solutions in this scenario? Installing Ubuntu on one of two hard drives Given a set $\mathcal{S}$ of size $n$, let a $k$-partition of $\mathcal{S}$ be a grouping into $k$ disjoint classes $$(S_1 ,S_2,...,S_k)$$   Where the $S_i$ do not necessarily contain the same number of elements.  Let $C(S_1, S_2, ... S_k)$ be the set of combinations which can be made by taking exactly one element of each class, (i.e. $C(S_1, S_2, ... S_k)$ is the Cartesian Product $S_1 \times S_2 \times ...\times S_k$). For a given $(n,k)$, what is the minimum number of k-partitions $N$ such that  $\bigcup\limits_{i=1}^{N} C(S_1^{(i)}, S_2^{(i)}, ...,S_3^{(i)}) = $ All Possible Combinations  Example:  for $n=4$ and $k=2$, $\mathcal{S} = \{1,2,3,4\}$ we can choose:  $$ S^{(1)} = \left\{\left\{ 1, 2\right\}, \left\{ 3, 4\right\}\right\}$$ $$ S^{(2)} = \left\{\left\{ 1, 3\right\}, \left\{ 2, 4\right\}\right\}$$  Then $$C_{1} = \left\{\left\{ 1, 3\right\} ,\left\{ 1, 4\right\},\left\{ 2, 3\right\},\left\{ 2, 4\right\}\right\}$$ $$C_{2} = \left\{\left\{ 1, 2\right\} ,\left\{ 1, 4\right\},\left\{ 2, 3\right\},\left\{ 3, 4\right\}\right\}$$  and $C_1 \cup C_2 =$ All possible combinations and $N=2$.