What is an Isomorphism: Linear algebra
What does "isomorphic" mean in linear algebra?
View only the new entries in a growing log file Show that both mixed partial derivatives exist at the origin but are not equal $$f(x,y) = \begin{cases} \displaystyle \frac{xy(x^2-y^2)}{x^2+y^2} &amp; \text{if } (x,y) \neq (0,0), \\ 0 &amp; \text{if } (x,y) = (0,0). \end{cases}$$ I tried finding both mixed partial derivatives but they ended up being the same for that function. I must be failing to take into account something dealing with the fact that it is piece-wise. I still need to show the mixed partial derivatives exist. How can I do all of this? MikTeX 2.9, install packages on the fly? Where can I find the points per game throughout many NBA seasons? Where can I find the points per game (of both teams) throughout many NBA seasons?  To illustrate my point, what I mean is something like:   2000/01 average points per NBA game: 200; 2001/02 average points per NBA game: 210; 2002/03 average points per NBA game: 205;   so on... Schrödinger Equation for Two Electrons? I'm having trouble finding a simple answer to this question (maybe because there isn't one), but I'm just confused about how the Schrödinger Equation would look for two electrons. I understand that it would exist in 6 dimensional configuration space, but how does the potential look? It's confusing that the potential would be different for each electron depending on where the other one is. Choice function for collection of arbitrary finite sets. AC required? \hfill \break does not work Formatting should not count towards the character limit on comments Surface tension: the paper clip experiment In the paper clip experiment, the surface tension of water prevents the clip from falling, thus we can assume it exerts a force of $mg$ (weight of clip) upwards.   However, if you try to pull the clip out of water, surface tension opposes this motion also. If for simplicity we assume that the clip is a rectangle of length $l$ and breadth $b$, and the surface tension is $T$, then the liquid exerts a downward force of: $$T×2(l+b)$$  What is going on here? Why is there an inconsistency in the direction along which the force acts? Join tables from two different server vertical alignment of a turned cell I know using turn command and a sample code like this:  \usepackage{rotating}  \begin{turn}{90} Supervised Learning \end{turn}}   we can rotate a text inside a cell, however, I couldn't find a way to vertically center this rotated text. Any suggestions is appreciated.  Here is the sample MWE:  \begin{table}[]     \centering     \begin{tabular}{|&gt;{\centering\arraybackslash}m{0.5cm}|c|&gt;{\centering\arraybackslash}m{8cm}|}         \hline         \multicolumn{2}{|c|}{Classification} &amp; References \\ \hline         %\multirow{2}{*}{{\begin{turn}{90}Supervised Learning\end{turn}}}            \multirow{2}{*}{\rotatebox[origin=c]{90}{Supervised Learning}}  \end{tabular}     \caption{A Classification}     \label{tab:Machine_Learning_models} \end{table} Is there a way to make Git mark a file as conflicted? Difference between Sort and SortBy Why do we say "try and" [verb] instead of "try to" [verb]? (E.g., "Try and call me tomorrow.") I know that an easy to handle formula for the CDF of a normal distribution is somewhat missing, due to the complicated error function in it.  However, I wonder if there is a a nice formula for $N(c_{-} \leq x &lt; c_{+}| \mu, \sigma^2)$. Or what the "state of the art" approximation for this problem might be. Can't install any app, App Store asks for credit card I haven't been installing anything on my iPad Mini for the past few weeks. But previously, I just had to tap on "Install", enter my Apple ID password and go.  Now, for every new application, even those free ones, I have to confirm each time, that I'm 17 or over. And then App Store asks to enter my credit card information. If I disagree and hit "Cancel", installation process is interrupted and I can't install any application, even free one.  I don't trust Apple at all and I'm not willing to share my credit card information, especially that I'm installing only free applications.  I'm pretty sure that I haven't changed anything in the configuration of my iPad Mini for ages.   Am I missing some significant change to the App Store or this is some kind of bug or virus? Is there anything I can do in this situation? How can I install a free application from the App Store, without having to share my credit card information with Apple? "invalid EFI file path" while booting Windows How do I quickly switch between weapons and spells? When  I see him quickly change his weapons and spells during combat. When he later goes inside his items, you can see a second smaller arrow next to the weapon that you can quickly change to in combat. How can I set such an alternative so that I can quickly switch weapon?  The screen doesn't seem to intuitively explain what key I need to use to do that... Installing from source - do I need to keep the extracted tarball directory If I'm installing from source, do I need to keep the extracted tarball directory?  So if I download the git tarball. I then do:  tar -xvzf git.tar.gz   This will create a git.x.x. directory, into which I cd, then run ./configure etc. Once I'm done with this process, and git, or whatever is installed, do I need to keep the original git.x.x extracted directory, or is that just used for compiling the program?  I'm somewhat confused by all the directories, and folders used for programs. I have created multiple objects, while testing I applied a drop shadow style on one object and its looking very good. Now I want to apply the same style to all other objects (around 20). Is there any way like global color to create a style once and apply to other objects with single click automatically?  Or I have to apply that drop shadow effect on each object one by one manually?