I am taking a course on multivariate statistics and I enjoy it pretty much. But I feel the course focuses too much on procedures and not on answering "why" some things are the way they are.  So let me be more specific. The course is about: - Exploratory and confirmatory factor analysis - Principal Component Analysis - Cluster Analysis - MANOVA - Canonical Correlation Analysis - Discriminant Analysis - Logistic Regression  We are currently following the book "Applied Multivariate Techniques" by Subhash Sharma. I would like to read a book which explains "why" things are the way they are. For example, instead of just saying "We apply the following test", I would like to know what the test statistic means and how we found it. I hope this makes sense.  It can be very mathematically rigorous, I don't mind. It doesn't have to be very proofy (although that would be neat!), but I would like to get to know "why" and not only "how".
I need a graduate level, mathematically rigorous textbook on multivariate analysis and inference to enhance myself. I've been reading the  and doing the problems within, but I need a book with other focuses. Topics like famous distributions (Wishart, Wilks lambda, etc.), hypothesis testing, some theory on estimation (point, interval), and other more modern materials are welcome. I've checked , but the OP there was looking for something useful for his psychological analysis, which is not exactly what I want here. Currently I have the , so I would also like to hear the comments about this book and its exercises. Thank you.
cat files with directory Is there a command to show the directory/file name when cat files?  For example: assume two files f1.txt and f2.txt are under ./tmp  ./tmp/f1.txt ./tmp/f2.txt    Then when I do cat ./tmp/*.txt, only the content of files will be shown. But how to firstly show the file name, then the content?, e.g.:   (The needed command):  ./tmp/f1.txt:    This is from f1.txt  and so on  ./tmp/f1.txt:  This is from f2.txt ...   Is there a command to do it? (There seems to be no option for 'cat' to show the file names) What is the function of this circuit? Just wondering if someone can give me an explanation for this capacitor layout - what is it's function? The chip to the right is an ADC.  Circled in blue.    I'm guessing it is well known but i don't know how to search for it. Why can't a Federation Starship's transporter history be used to bring someone back to life? using a class defined in a c++ dll in c# code I have a dll that was written in c++, I need to use this dll in my c# code. After searching I found that using P/Invoke would give me access to the function I need, but these functions are defined with in a class and use non-static private member variables. So I need to be able to create an instance of this class to properly use the functions. How can I gain access to this class so that I can create an instance? I have been unable to find a way to do this.   I guess I should note that the c++ dll is not my code. What should I do when my neural network doesn't learn? I'm training a neural network but the training loss doesn't decrease. How can I fix this?  I'm not asking about overfitting or regularization. I'm asking about how to solve the problem where my network's performance doesn't improve on the training set.    This question is intentionally general so that other questions about how to train a neural network can be closed as a duplicate of this one, with the attitude that "if you give a man a fish you feed him for a day, but if you teach a man to fish, you can feed him for the rest of his life." See this Meta thread for a discussion:   If your neural network does not generalize well, see: Introduction to string theory I am in the last year of MSc. and would like to read string theory. I have the Zwiebach Book, but along with it what other advanced book can be followed, which can be a complimentary to Zwiebach. I would like a more mathematically rigorous book or lecture notes along with Zwiebach.   Specifically, mention whether the book discusses string theory   Rigorously? Intuitively?   What's the scope of the book? Does it cover the advanced materials, e.g. Matrix string theory, F-theory, string field theory, etc. Maybe even String Phenomenology? I know you can create a rounded-corner rectangle; but, how do you create a triangle with rounded corners in Photoshop?  I am actually interested in making it from scratch, not basing it on a custom shape that is available in Photoshop. Thanks. Did I derive a new form of the gamma function? Allow suppression of automatic linking of web addresses How can I randomise the output of a redstone circuit? I have 5 buttons and only one of these can be correct, all others must be false. These 5 outputs will go into 2 outputs, in between there needs to be a circuit which changes which single button out of the 5 will go down the &quot;correct&quot; output of the final 2. The 4 remaining buttons must go to the second of the final 2 outputs. Both final outputs must give out a true signal for a brief period the same as a button on its own would produce. There should also be a way of activating the circuit. Not sure if that is explained well enough so I have made a basic diagram of what I need.  The diagram shows how I need the signal to be split. However in between the buttons and the final two wires there needs to be a circuit (marked by the grey box). This circuit changes the single button connected to the left wire. The right input should start the circuit and randomise the 5 buttons. There are no limits to size, amount of materials used or method used. This question is similar to the one asking about , but I am specifically working with Redstone circuitry - the commands solutions do not apply here Suppose $A$ is a general $n \times n$ matrix and $B$ is obtained by interchanging two rows of $A$. Prove that $\det(B) = -\det(A)$ Suppose that $A$ is a general $n \times n$ matrix and $B$ is obtained by interchanging the first two rows of $A$. Prove that $\det(B) = -\det(A)$.  By general $n \times n$ matrix, I mean $$\left[\begin{matrix} a_{11} &amp; a_{12} &amp; \cdots &amp; a_{1n} \\ a_{21} &amp; a_{22} &amp; \cdots &amp; a_{2n} \\ \vdots &amp; \vdots &amp; \ddots &amp; \vdots \\ a_{n1} &amp; a_{n2} &amp; \cdots &amp; a_{nn} \end{matrix} \right]$$ I'm thinking of using the cofactor expansion of the 2nd row of the first matrix, yielding $$ \det(A) = c_{21} a_{21} + c_{22} a_{22} + \cdots+ c_{2n} a_{2n}  $$ which will be positive or negative depending on $n$ and the values of $a_{21}, \ldots,a_{2n}$, and using the same on the first row in matrix $B$ to get $c_{11} a_{21}$ etc. and then use the fact that the power of the $c$ subscripts will alter $\det(B)$ to be the opposite sign, but I'm not sure how to express all of this mathematically in a proof directly. Help please? How can I use an align environment flush left? Is there a way possible to imitate the align environment for math mode commands, without having all writing being placed toward the center on the output page?  MWE:  \documentclass{article} \usepackage{mathtools}  \begin{document} \begin{align*} \cos\theta_1 \cos\theta_2-\sin\theta_1\sin\theta_2 &amp;= \cos(\theta_1 +\theta_2) \\ \sin\theta_1 \cos\theta_2 + \cos\theta_1 \sin\theta_2 &amp;= \sin(\theta_1+\theta_2) \end{align*}  \end{document} Using Laptop Screen as a monitor What to do when I get an "attempt to read or write outside of disk 'hd0'" error and Boot Repair does not solve the problem? Update Manager doesn't ask for a password Oneiric update manager no longer asks for a password to update already installed software.  This is a change in behavior from previous versions.  Is there a way to revert this behavior and get the Update Manager in Oneiric to ask for a password again?  Thanks! Stop jQuery .load response from being cached I have the following code making a GET request on a URL:  $('#searchButton').click(function() {     $('#inquiry').load('/portal/?f=searchBilling&amp;pid=' + $('#query').val());             });   But the returned result is not always reflected. For example, I made a change in the response that spit out a stack trace but the stack trace did not appear when I clicked on the search button. I looked at the underlying PHP code that controls the ajax response and it had the correct code and visiting the page directly showed the correct result but the output returned by .load was old.  If I close the browser and reopen it it works once and then starts to return the stale information. Can I control this by jQuery or do I need to have my PHP script output headers to control caching? With me going it alone in development I only have limited resources at my disposal i.e one pc with which I develop and test the game. so I only know for certain my game works with that setup.  What options have I got in testing the game on the many different hardware/operating system combinations? Its a windows desktop game. Can someone explain Cayley's Theorem step by step? This is from Fraleigh's First Course in Abstract Algebra (page 82, Theorem 8.16) and I keep having hard time understanding its proof. I understand only until they mention the map $\lambda_x (g) = xg$. Can someone explain this proof step by step? Thank you so much! Here is the proof:  Let $G$ be a group. We show that $G$ is isomorphic to a subgroup of $S_G$. Define a one-to-one function $\phi: G \to S_G$ such that $\phi(xy)=\phi(x) \phi(y)$ for all $x,y \in G$. For $x \in G$, let $\lambda_x: G \to G$ be defined by $\lambda_x (g) = xg$ for all $g \in G$. The equation $\lambda_x (x^{-1} c) = x(x^{-1} c) = c$ for all $c \in G$ shows that $\lambda_x$ maps $G$ onto $G$. If $\lambda_x (a) = \lambda_x (b)$, then $xa=xb$ so $a=b$ by cancellation. Thus $\lambda_x$ is also one to one, and is a permutation of $G$. We now define $\phi: G \to S_G$ by defining $\phi(x) = \lambda_x$ for all $x \in G$. To show that $\phi$ is one to one, suppose that $\phi(x) = \phi(y)$. Then $\lambda_x = \lambda_y$ as functions mapping $G$ into $G$. In particular $\lambda_x (e) = \lambda_y (e)$, so $xe=ye$ and $x=y$. Thus $\phi$ is one to one. It only remains to show that $\phi(xy) = \phi(x) \phi(y)$, that is, that $\phi_{xy} = \lambda_x \lambda_y$. Now for any $g \in G$, we have $\lambda_{xy} (g) = (xy)g$. Permutation multiplication is function composition, so $(\lambda_x \lambda_y)(g) = \lambda_x (\lambda_y (g)) = \lambda_x (yg) = x(yg)$. Thus by associativity, $\lambda_{xy} = \lambda_x \lambda_y$. Answer turned to CW, votes pre-CW era doesn't count in tag specific stat My understanding is that if an answer becomes CW (one way or another), original author gets to keep the votes pre-CW.  Does this also keep the pre-CW vote count for the tag-specific stat? It doesn't look like it, because I checked recently and suddenly my number dropped. It looks like the tag-specific stat just counts votes for non-CW answers, and doesn't "discriminate" between the pre-CW and post-CW era. If it's eventually CW, then it simply contributes 0 votes.  I'm fine with the fact that my answer became CW (in this case, through the question having 30+ answers), but I would like to keep the votes I earned before it did for the tag stat.  Otherwise I think the system is "broken". Someone can go posting 30+ answers to questions where Jon Skeet answered, and all of Jon Skeet's answers would become CW, and he'd then be 0 at all tags. In other words, can I do something like  for() {     for {        for {        }     } }   Except N times? In other words, when the method creating the loops is called, it is given some parameter N, and the method would then create N of these loops nested one in another?  Of course, the idea is that there should be an "easy" or "the usual" way of doing it. I already have an idea for a very complicated one.