Before, I ask similar this. But here I change question settings since it was incomplete. I hope receive good ideas.  Let $E$ be a finite dimensional vector space over field $\mathbb R$ with $E^*$ as the dual space of $E$ and $E^{**}:=(E^*)^*$ is the double duall of $E$. ($\dim E=n$)   $Alt^P(E):=\{ \alpha\colon \overbrace{E\times\cdots\times E}^{p- times}\rightarrow \mathbb R\  \ , \alpha \text{ is alternating multilinear map}\}$ $Alt^P(E^*):=\{ u\colon \overbrace{E^*\times\cdots\times E^*}^{p- times}\rightarrow \mathbb R\  \ , u \text{ is alternating multilinear map}\}$  I wish to prove that there exist an $\textbf{unique}$ bilinear form $B\colon  Alt^p(E^*)\times Alt^p(E)\rightarrow\mathbb R$   such that for all $ f_i\in E^* \ , u_j\in E^{**}\stackrel{\scriptsize{isomorph}}\simeq E \qquad  i,j=1,\cdots,p$, it has the following rule:  $B(u_1\wedge\cdots\wedge u_p,f_1\wedge\cdots\wedge f_p)=\det[f_i(u_j)]$.  $\wedge$ is wedge product between alternating maps i.e. $\alpha\wedge\beta(v_1,\cdots,v_{p+p})=\dfrac{1}{p! p!}\displaystyle\sum_{\sigma\in S_{p+p}}sign(\sigma)\alpha(v_{\sigma(1)},\cdots,v_{\sigma(p)})\beta(v_{\sigma(p+1)},\cdots,v_{\sigma(p+p)})$  How can I do this?
Let $E$ be a finite dimensional vector space over field $\mathbb R$ with $E^*$ as the dual space of $E$.($\dim E=n$)   $\Omega^P(E):=\{ \alpha\colon \overbrace{E\times\cdots\times E}^{p- times}\rightarrow \mathbb R\  \ , \alpha \text{ is alternating multilinear map}\}$ $\Omega^P(E^*):=\{ u\colon \overbrace{E^*\times\cdots\times E^*}^{p- times}\rightarrow \mathbb R\  \ , u \text{ is alternating multilinear map}\}$  I wish to prove that there exist an $\textbf{unique}$ bilinear form $B\colon \Omega^p(E^*)\times\Omega^p(E)\rightarrow\mathbb R$   such that for all $ f_i\in E^* \ , u_j\in E^{**}\simeq E \qquad  i,j=1,\cdots,p$, it has the following rule:  $B(u_1\wedge\cdots\wedge u_p,f_1\wedge\cdots\wedge f_p)=\det[f_i(u_j)]$.  $\wedge$ is wedge product between alternating maps i.e. $\alpha\wedge\beta(v_1,\cdots,v_{p+p})=\dfrac{1}{p! p!}\displaystyle\sum_{\sigma\in S_{p+p}}sign(\sigma)\alpha(v_{\sigma(1)},\cdots,v_{\sigma(p)})\beta(v_{\sigma(p+1)},\cdots,v_{\sigma(p+p)})$  How can I do this?
Event binding on dynamically created elements? "Can/may/will you help me with this?" Which word to use when we ask for help?  Some conditions:     We know that the person asked is able to do it. We don't know if the person asked is able to do it. I'm using a custom class file.  My main file looks like this:  \documentclass[12pt,a4paper]{thesis} \begin{document} \frontmatter     \pagenumbering{alph}      \pagenumbering{roman}     \clearpage      \cleardoublepage     \tableofcontents     \clearpage     \listoffigures     \clearpage     \listoftables   \mainmatter        \part{test}       \input{test} \end{document}   If I put this in my test.tex it does work:  \chapter{test} \label{chapter:test} test    When it becomes more text (lets say 40x the word "test") I get the error stated in my question title.  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Can I travel with them with only the permesso di soggiorno? For me the distinction between sites is purely topical. I get that there's a right and a wrong place to ask questions, but I regularly ask questions across a number of sites. They all log me in (in a weird sort of way), and now there's the global inbox.  I've read that there's a feed  and that there's a  but neither of these are what I want.  What I'd like is to have an RSS feed from my global inbox, i.e. to include notification of updates to my public questions, answers, comments. Is this possible? I've logged in and out, restarted my phone, updated, but the Pokemon footsteps indicating whats nearby wont show up.   The Pokemon still appear in the menu, but I cannot click to select them, nor does it show their distance from me with the footsteps.   What is going on? Wrong ordering in generated table in jpa How to generate XML file dynamically using PHP? So, after a few sessions, the new player I'd invited has been a bit of a disaster. He doesn't get on well with any of the other players, laughed when someone's character died (in our campaign that's permanent at the moment), and generally has been a nuisance. However, he doesn't seem to notice this. I've talked to him about his behaviour, but it hasn't helped. Several other players have also approached me on their own to register concerns.  The long and short of it is, he's not a good fit for our game or social group, due to his abrasive personality/playstyle (as I and the other players perceive it). He's also not interested in roleplaying (something my group does heavily, at the moment) and continually pushes to place himself in the limelight - which he does by instigating combat and trying to skip over what he sees as 'boring' scenes. 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