I want to have two matrixes of $ A $ and $B$ of a certain size, multiply them together $C = AB$, do some operations on $C$ to make $C_2$ and then decompose the matrix into to matrices of the same size as $A$ and $B$ so that $A_2B_2 = C_2$.  Which decomposition function can I use to achieve this?  EDIT: This is not a duplicate because the thread linked in the comments using LU decomposition says nothing about L and U being the same dimensions as the original matrix
Wikipedia says "In the mathematical discipline of linear algebra, a matrix decomposition or matrix factorization is a factorization of a matrix into a product of matrices. There are many different matrix decompositions; each finds use among a particular class of problems."  But in my opinion decomposition term should be used to represent breaking a matrix in different sub-matrices or some new matrices created after some operation on original matrix which if used together and passed through some algorithm(not necessarily product), shall reproduce the original matrix.  Is there some different terminology to represent what I am expecting to say?
Performance of try-catch in php What kind of performance implications are there to consider when using try-catch statements in php 5?   I've read some old and seemingly conflicting information on this subject on the web before. A lot of the framework I currently have to work with was created on php 4 and lacks many of the niceties of php 5. So, I don't have much experience myself in using try-catchs with php. Let $R$ be a simple ring and $T$ be a non-zero ring. Let $f\colon R \rightarrow T$ be a ring homomorphism. Show $f$ is injective.  Proof: $\ker f \lhd R$, so $\ker f=R$ or $\ker f=\{0\}$. If $\ker f=R$ then $R/R \cong \{0\}$, but $T \neq \{0\}$, which is a contradiction. I can't see why does the last part means contradiction.   Thanks for any assistance! Using the inference of mean as an example, the null and alternative hypothesis could be  $$H_0: \mu \le 0 \Leftrightarrow H_1: \mu &gt; 0$$  It is often argued that this makes the calculation of the $p$-value (or critical region) easier, but from my understanding the $p$-value is $P(\bar{X} &gt; 0|H_0) \stackrel{\color{red}{?}}{=} \sup_{\theta \in H_0} P(\bar{X} &gt; 0 | \theta )$. Since I'm taking its supremum, the $p$-value doesn't change regardless of whether the equality sign is included. The same result goes for the critical region. However, I'm not sure if my understanding is correct, and my doubt is marked with a red question mark above.  Anyway, I wonder if it's correct (I know that would be unconventional, though) to write  $$H_0: \mu &lt; 0 \Leftrightarrow H_1: \mu \ge 0$$  If that's OK, what about its $p$-value and critical region? If that's not OK, I would be really surprised, because in that way we are changing the question ("Is $\mu$ less than or equal to zero?") to something different ("Is $\mu$ less than zero?") I have a 17 inch LCD, with a maximum resolution of 1280x720. It works fine, but there are some apps that require 1024x768. I know that the maximum resolution is called like that for a reason, but is there no way of increasing the resolution, other than getting a bigger monitor? How do I access my Windows partition? I have Ubuntu 12.04 installed on my HP G62-453 TU Laptop. I cannot access the contents of my hard disk partition E. Since I've a database systems examination in less than 3 hours (from now), I have been browsing Stack Exchange network for questions with normalisation and related tags. Most of the questions are now closed as  or others from the list.  Since, these questions are closed, no users are allowed to post answers to them (unless they are reopened). Why am I, then, allowed the option to protect such questions? Doesn't that beat the entire purpose behind "protecting" a question? How well will WCF scale to a large number of client users? Does anyone have any experience with how well web services build with Microsoft's WCF will scale to a large number of users?  The level I'm thinking of is in the region of 1000+ client users connecting to a collection of WCF services providing the business logic for our application, and these talking to a database - similar to a traditional 3-tier architecture.   Are there any particular gotchas that have slowed down performance, or any design lessons learnt that have enabled this level of scalability? "A number of students" vs. "the number of students" Possible Duplicate:          From the grammatical view both are correct, but please explain the difference in meaning:   The number of students in the class is fifteen. A number of students were late for class. 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The only way I can get it to show at all is by specifying the H placement specifier, but that places the image inside the text where I defined it, not on top of the column.  This is my best try, but it hides the image and breaks all references to ??:  \begin{figure}[t!]   \centering     \includegraphics[width=0.25\textwidth]{figure}   \caption{Dataflow pipeline of the edge detector}   \label{fig:workflowedge} \end{figure}   and I'm getting the warning:  Package multicol Warning: Floats and marginpars not allowed inside `multicols' environment!.   How can I make a figure a non-float?  I also tried the figure* environment, but that just creates an image centered on top of the page, like my first point. QGIS ->ArcGIS Server configuration possible? SharePoint Current User View using JavaScript How do I backup data (SMS/contacts) from a device with a broken screen? I just broke the screen of my (unrooted) Galaxy S.  How do I get back my SMS and contacts?   PS: I tried Kies but it won't detect my phone for some reason. (Kies works fine with another Galaxy I possess but not this one) Google Chrome can't play some flash videos Some flash videos won't play in Chrome, while they play perfectly in other browsers. The player will load, but instead of showing a preview of the video and a play button on the middle of the video, the screen is black:    Here's an example of a  and here is a . The video that works is a Youtube video embedded on the site with , while the nonworking one is probably hosted by the website itself. In both cases it is using Flash. The site is popular and others don't seem to be experiencing this problem.  I am running Win7 64bit and I have no ad blockers installed.  I have found two common solutions to this problem, neither of which work:  Solution #1: .  Solution #2: .  Any suggestions? My question is related to my previous asked one:   I have about 300 shapekeys and want to set the random value for all of them . How to do it using scripting? Teenagers find an ancient lizard creature in stasis and accompany him on adventures to an undersea city When I was a kid, I read a book (likely from the '60s) about a pair of kids who find an ancient lizard/fish man inside a cave. The cave has been recently exposed by an earthquake and the creature is inside a super technologically advanced stasis chamber. I think this creature's name is something like "Sslaa". He takes the kids on a quest to find his lost underwater city.  They end up finding the city, which is still populated by creatures like himself and protected from the ocean above by an immense diamond dome. Eventually, Sslaa has to drive an advanced mining vehicle deep into the crust of the earth, presumably to prevent his city's destruction by an impeding magma flow or other seismic event.  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For me, I have set this as:  export EDITOR="/usr/local/bin/mvim"   With aliases for that editor using the -v flag which loads vim in the terminal:   mac_vim="$EDITOR -v"  alias vi=$mac_vim  alias vim=$mac_vim  alias v=$mac_vim   That works but when the gcloud CLI calls $EDITOR it does not have the -v flag so it opens in a new terminal.  I thought I could change that by instead adding the -v flag here:  export EDITOR="/usr/local/bin/mvim -v"   However, when I try and run that on the command line I get:  $EDITOR text.html zsh: no such file or directory: /usr/local/bin/mvim -v   Is it possible to include a flag when exporting my $EDITOR? (Up to / until / by) 50% off I wonder if someone could tell me which choice works in the following sentence and why the others do not work: (From my point of view, all of these choices work in this context.)  They have great promotion till January 5th......50% off. a) up to; b) until; c) by