\documentclass{article}  \begin{document}  ${x_i}^j$ works as expected but not with an hat as in ${\hat{x}_i}^j$. The way I found to make it work is $\mbox{$\hat{x}_i$}^j$.  Is there an nicer solution?   \end{document}
124241
I like how there is a gap between the subscript and the superscript when I write ${w_i}^T$. However, if I try to put a hat on the vector, like $\hat{w}_i^T$, this space goes away. Any ideas?  I tried putting in an extra set of braces, as suggested for a similar question , but it didn't work.
97639
How do I write x^x^x^x^x^x^x^x^x^x?   My LaTeX distribution doesn't wanna eat it, it stops swallowing stuff at the double power x^x^x. What I'm aiming at is essentially building a telescope out of X's stacked on top of each other. Don't ask, that's my sense of humour.
97319
Can you please explain why \begin{align*} \lim_{x\to 0^+}{x^{x^x}} &amp;= 0 \end{align*}
62357
How can I write e^(3j) in LaTeX?  I have tried many syntax, like $e^(3j)$ or $e^*{3j}$  Any help will be very well received.
62475
I have the following MNWE and don't understand why this fails.   \documentclass{article} \usepackage{amsmath} \begin{document} $\dots \left. \right.$ \end{document}   Understanding the relevant code in amsmath proves to be rather difficult and I can't find a mention anywhere that this is somehow not OK to do. Of course I can use some of the more specialized dot commands to get rid of the guessing \dots does. I would be extra grateful for an explanation of what the trick with \uppercase in all the helper definitions(\striplong@...) and using \meaning in \mdots is.
107200
I am trying to typeset he following inline math for a camera-ready document:  $\hat{\boldsymbol \Sigma}_{P}^{-1} \hat{\boldsymbol \Sigma}_{G}$   It appears that the superscript -1 is aligned considering \Sigma and the \hat symbol as  complete item. This increases the line spacing. What I would like to typeset is the -1 aligned with \Sigma only, i.e. to move it downward a little. Is that feasible and, if so, how can this done?
72027
Normally, most people use the symbol $\Box$ to represent the  (including the linked to Wikipedia page).  Recently I wanted to use \hat\Box and \tilde\Box, but they do not render very well.    What is the "best" way to create such symbols?    Aside: The above image is rendered using my local install of pdflatex: pdfTeX 3.1415926-1.40.10-2.2 (TeX Live 2009/Debian). The symbols seem to render fine on some online services: e.g. "" produces    from   \begin{align*} \Box &amp;= \sum_a \partial^a\partial_a \,, &amp; \hat\Box &amp;= \sum_a \mathcal{D}^a\mathcal{D}_a \end{align*}
34589
Forgive my ignorance. The below seems 'inconsistent'. If canceling the $(x+1)$ is 'legal', how does the domain change? I realize it does, but would someone be so kind as to provide an explanation?    $$ \frac{x^2 - 1}{x + 1} \mbox{ is undefined when } x = -1 $$  Its domain (the values that can go into the expression) does not include $ -1 $.  Now, we can factor $ x^2 - 1 $ into $ (x - 1)(x + 1) $ so we get:  $$ \frac{(x - 1)(x + 1)}{(x + 1)} $$  It is now tempting to cancel $ (x + 1) $ from top and bottom to produce:  $$ x - 1 $$  $$ \mbox{Its domain now } \textbf{does} \mbox{ include } -1 \mbox{.} $$  But it is now a different function because it has a different domain.    Thanks!
12759
Consider the following MWE.  \documentclass[preview,border=12pt,varwidth]{standalone} \usepackage{amsmath}  \begin{document} \abovedisplayskip=0pt\relax \begin{equation} \begin{cases} ax + by =c \\ px + qy = r \end{cases} \end{equation} \end{document}   produces an output as follows.    What I want to achieve is as follows.    Is there any idea?  My attempt is as follows, but it does not compile.  \documentclass[preview,border=12pt,varwidth]{standalone} \usepackage{amsmath}  \begin{document} \abovedisplayskip=0pt\relax \begin{equation} \begin{cases} ax + by =c \tag{OK}\\ px + qy = r \tag{Yes} \end{cases} \end{equation} \end{document}
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I would like to put something at the top of the \longrightarrow, something like \longrightarrow^{k\rightarrow\infty}. However, instead of putting k\rightarrow\infty on the top right corner, I would like to put it in the middle on the top of \longrightarrow. Could someone help me?
71857
Help me find $\hat{B^\dagger}$, when we know that $$\hat{B}=i\frac{d}{dr}$$ with the condition that $\hat{B}$ is defined in spherical coordinates. My approach: $$ \langle\psi|\hat{B}\psi\rangle=\int_{0}^{\infty} \psi^* i\frac{d}{dr} \psi dr=\psi^*\psi|_{0}^{\infty}-\int_{0}^{\infty}\psi i\frac{d}{dr}\psi^*dr=\langle\hat{B}\psi|\psi^*\rangle$$ And so I get $ \hat{B^\dagger} = -i\frac{d}{dr} $. Could someone confirm if this is correct?
67651
Is it possible in Latex to make a triangular hat? The one that is used in math over three letters representing points to indicate a triangle.  Something like:
53433
Prove that $$\nabla_{\mathrm X} \mbox{tr} (\mathrm A \mathrm X^{-1} \mathrm B) = - \mathrm X^{-\top} \mathrm A^\top \mathrm B^\top \mathrm X^{-\top}$$   My proof is below. I am interested in other proofs.    My proof  Let   $$f (\mathrm X) := \mbox{tr} (\mathrm A \mathrm X^{-1} \mathrm B)$$  Hence,  $$\begin{array}{rl} f (\mathrm X + h \mathrm V) &amp;= \mbox{tr} (\mathrm A (\mathrm X + h \mathrm V)^{-1} \mathrm B)\\ &amp;= \mbox{tr} (\mathrm A (\mathrm X ( \mathrm I + h \mathrm X^{-1} \mathrm V))^{-1} \mathrm B)\\ &amp;= \mbox{tr} (\mathrm A ( \mathrm I + h \mathrm X^{-1} \mathrm V)^{-1} \mathrm X^{-1} \mathrm B)\\ &amp;= \mbox{tr} (\mathrm A ( \mathrm I - h \mathrm X^{-1} \mathrm V + O (h^2)) \mathrm X^{-1} \mathrm B)\\ &amp;= \mbox{tr} (\mathrm A \mathrm X^{-1} \mathrm B) - h \, \mbox{tr} ( \mathrm A \mathrm X^{-1} \mathrm V \mathrm X^{-1} \mathrm B) + O (h^2)\\ &amp;= f (\mathrm X) - h \, \mbox{tr} ( \mathrm X^{-1} \mathrm B \mathrm A \mathrm X^{-1} \mathrm V ) + O (h^2)\end{array}$$  Thus, the directional derivative of $f$ in the direction of $\mathrm V$ at $\mathrm X$ is  $$D_{\mathrm V} f (\mathrm X) = - \mbox{tr} ( \mathrm X^{-1} \mathrm B \mathrm A \mathrm X^{-1} \mathrm V ) = - \mbox{tr} ( (\mathrm X^{-\top} \mathrm A^\top \mathrm B^\top \mathrm X^{-\top})^\top \mathrm V ) = - \langle \mathrm X^{-\top} \mathrm A^\top \mathrm B^\top \mathrm X^{-\top}, \mathrm V \rangle$$  and, lastly,  $$\nabla_{\mathrm X} \mbox{tr} (\mathrm A \mathrm X^{-1} \mathrm B) = - \mathrm X^{-\top} \mathrm A^\top \mathrm B^\top \mathrm X^{-\top}$$
5557
The mapping is supposed to be from $\mathbb{N}$ to $\mathbb{N}$.  I'm still trying to understand if this is possible, I mean if it was from $\mathbb{R}$ to $\mathbb{N}$, I guess $x^2$ would work.
56104
It seems to me that my method is quite inconvenient.  Could someone help me in this matter?      \documentclass[11pt,a4paper]{article}     \usepackage{blindtext}     \usepackage{mathtools}     \DeclareMathOperator{\sgn}{sgn} \begin{document}     $\begin{vmatrix}     a_{11} \cdots a_{1r}\cdots a_{1n}\\     \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \dots \cdot \cdot \cdots \cdot \\     a_{n1} \cdots a_{nr} \cdots a_{nn} \end{vmatrix}$ \end{document}
109693
What is the difference between \text, \textrm, \textnormal, and \mbox (and possibly other commands commonly used to produce text in math mode)?  Various (La)TeX tutorials teach different methods, and I am sure that there is either a best one or there are subtly different usage scenarios.
44253
Is there a canonical way to typeset such quantities in equations and inline math?  \documentclass{article} \begin{document} $Re$, $Nu$ are clearly not an option. $\mathit{Re}$, $\mathit{Nu}$ appear ok to me. \end{document}