Let us have two matrices: $A,B$ which are both $n$ x $n$ type, and $AB+A+B=0$ stands. Prove, that in this case, $AB = BA$.  I tried to do such matrices, and the statement stands, but how should I do a proving in general? Thanks!
Given matrices $A$ and $B$, where that $AB = A + B$, prove $AB = BA$. I keep coming up with AB = AB. It seems like basic algebra, but for the life of me, I'm getting nowhere :/. Someone help please?
Unbiased Estimator for a Uniform Variable Support Let $ x_i $ be iid observations in a sample from a uniform distribution over $ \left[ 0, \theta \right] $.  Now I need to estimate $ \theta $ based on $N$ observations and I want the estimator to be unbiased.  I thought about simple estimator $ \hat{\theta} = \max \left( x_i \right) $.  Based on simulation it is not biased, yet I couldn't show it analytically.  Could anyone, please, show it is unbiased?  BTW, I could easily find another, easy to prove, unbiased estimator, $ \hat{\theta} = 2 \mathrm{mean} \left( {x}_{i} \right) $ How to delete all files in a current directory starting with a dot? Is it possible to mount a virtual hard disk (VHD, HDD, VDI, VMDK) on Ubuntu? How can this be done? Recursive time series forecasting model In a recursive forecasting model, let's say you are trying to predict sales of Target for the next month and you will append that prediction to your input and predict the month after. Basically, your target is Sales quantity, which you lagged. But let's say you have other continuous numerical features like Price which you will lag as well. As your model is making predictions on Sales_QTY, it will feed it back to sales_qty as input so you will never ran out of values for that one. So how do you deal with your other features (other than the target) in order to generate them as next months inputs in a recursive forecasting model (because eventually you will run out of them)? DO you create a sub-model and try to predict them as well? How to reinstall PulseAudio (Ubuntu 12.04) A question about $f(x)\equiv 0$ Removing the Bracket from the First Line of bmatrix How can I write a matrix with a header line that is not bracketed? I have used the following code to produce the results below. In addition of being ugly, it is impractical when I need to align the first row, n1, ..., n6 with the matrix columns.  \documentclass{book}  \usepackage{amsmath}    \begin{document}    \[ \ \ \ \ \ \ \ n_1\ \ \ \ \ \ \ \ n_2\ \ \ \ n_3\ \ \ \ \ \ \ \ \ n_4\ \ \ \ n_5\ \ \ \ n_6\]     \[ \begin{bmatrix}         1 &amp; -1 &amp; 0 &amp; 0 &amp; 0 &amp; 1\\         0.960 &amp; -0.977 &amp; 0 &amp; 0 &amp; 0 &amp; 0.983\\         0 &amp; 1 &amp; -1 &amp; -1 &amp; 0 &amp; 0\\         0 &amp; 0.977 &amp; 0 &amp; -0.983 &amp; 0 &amp; 0\\         0 &amp; 0 &amp; 0 &amp; 1 &amp; -1 &amp; -1\\         0 &amp; 0 &amp; 0 &amp; 0 &amp; 0 &amp; 1\\        \end{bmatrix}        \begin{bmatrix}n_1\\n_2\\n_3\\n_4\\n_5\\n_6\end{bmatrix} =        \begin{bmatrix}0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 100\end{bmatrix} \]  \end{document} Comprehensive book on group theory for physicists? How to make \left, \right pairs of delimiter work over multiple lines? How can I type a Unicode character (for example, em-dash —?) The title pretty much says it all: how can I type Unicode characters - specifically the em-dash —? Fastest Gun in the West Problem I feel like there's a problem with Stack Overflow, as the number of people prowling it increases.  Each question's answers are sorted by descending score and then by descending time of posting. This means that if a person sits down and answers a question in a long, thorough way, going through every nook and cranny, once they post their answer, it will already be one of about seven different ones, some of which have already been upvoted. This wouldn't be a problem if those answers were as thorough as the one this guy's posting, but they usually aren't. Some of them are downright wrong, some aren't even answers to the question asked because their poster didn't bother to read the question all the way through.  This causes a problem I like to call Stack Overflow's Fastest Gun in the West Problem. I've come to a point where I'd rather just send a short, simple, correct explanation, than to go and do some proper research, write a whole blog post about it or even make sure the code I post even compiles, just so it will be noticed, as opposed to the incorrect ones.  I'm sure I'm not the only one doing this and that it despairs many people from even trying to answer questions.  I've long ago learned to try to always raise a problem with a solution in hand, rather than just say "This is a problem, handle it," so my question, after this long tirade, is:     How do you think this can be changed? What would you change in Stack Overflow to make this problem go away without hurting the site?   I promise to vote on answers I like, even if it takes you a long while to post them. :) What is the format for e-mail headers that display a name rather than the e-mail? How do you reverse a string in C or C++ without requiring a separate buffer to hold the reversed string? Is there a performance difference between i++ and ++i in C++? We have the question   What's the answer for C++? What's the difference between align and align*? After some brief searching I can't find the difference between align and align*. Google summarily ignoring the * is making it harder I think.  Can you tell me the difference between these two?  Moreover, can you tell me where you generally go for this type of information? As a relatively new user I'm still building up my resources. What Did Lyanna Stark Say to Ned Stark? In the final episode of season 6 we see that Lyanna Stark is whispering something to Ned. What is she saying? Creating all possible line segments between all points using QGIS I read this sentence in a book:     I just took part in a study over in the Psychology Department.   Why do we add over in front of in the here? If I put my phone on my notebook's left corner, it shuts down. Can anybody give me reliable explanation as to why this is happening?? When I receive a message on an SE post, I get a notification like this:    If I double tap this notification, the SE application opens, but my feed is empty approximately half the time. It looks like this:    If I refresh the feed (slide from the top), the feed does refresh and shows the new notification.   The notification, above, leads to  comment.  I haven't figured out the pattern yet, but this occurs roughly half the time I open a notification. It's occurred for chat messages, comments and answers - but not consistently. I have received notifications for the same post (for example, the two comments after the one linked above) that do not show an empty feed. But, a chat message barely 10 minutes later will show the empty feed again.  I am utilizing the beta app - version 1.0.72 on Android 5.0.1.