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I need help with the following function:

$$ \rho(x,\theta)=\min_{\lambda\in [0,\infty]} d(x ,x+\lambda[\cos \theta, \sin \theta]^T),$$ such that $$ x+\lambda[\cos \theta,\sin \theta]^T\in \bigcup_i \mathcal{W}\mathcal{O}_i$$

  1. how to write the 'min' part?

  2. what does $\lambda [\cos \theta, \sin \theta ]^T$ mean?

  3. my question is not showing up as MathJax symbol. how can I do that?

vadim123
  • 82,796
CaTx
  • 171
  • Taking last things first, if you put a dollar sign at each end, you'll get $\lambda [\cos \theta, \sin \theta ]^T$. – Gerry Myerson Apr 27 '13 at 05:55
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    Welcome to Math.SE. Thank you for your question. We will be better able to help you if you provide context and definitions for $\mathcal{W}\mathcal{O}_i$, as well as details about what you've tried so far. – vadim123 Apr 27 '13 at 06:14
  • With regards to question #2, it seems that $x$ is meant to be a vector in $\mathbb{R}^2$, as is $[\cos \theta, \sin \theta]^T=\left[\begin{smallmatrix} \cos \theta\ \sin \theta \end{smallmatrix}\right]$. – vadim123 Apr 27 '13 at 06:15
  • thank you for the hearty welcome. vadim123, $\mathcal{W}\mathcal{O}_i$ denotes the $i^{th}$ obstable. – CaTx Apr 28 '13 at 03:21

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