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I have an input array of line segments $(a,b)_1 ... (a,b)_n$. Let's call it $S$ so $(a,b)_{S_1} ... (a,b)_{S_n}$.

I have another array of the same construct, let's call it $I$, so $a,b)_{I_1} ... (a,b)_{I_n}$.

I wish to mathematically express the shortest distance of each of $I$ against $S$. In other words, the matrix formed from the product of $I\ S$. To be very clear, each $I$ is compared to each $S$. I want the minimum.

I know $\|(a,b)_{I_k}-(a,b)_{S_k}\|$ denotes distance. How do I represent the matrix formed and indicate the Min of the cells?

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    "Indicate" = mathematically denote.2010-12-28

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Denote $(a,b)_{S_i}$ by $S_i$ and $(a,b)_{I_k}$ by $I_k$.

Distance between $i^{th}$ line segment of $S$ and $j^{th}$ segment of $I$ is $|| (S_i,\ I_j) ||$.

You can now denote the minimum by

$ \text{min}_{1 \le i \le n,1 \le j \le n} \{|| (S_i,\ I_j)||\}$

Or you can denote the matrix by

$M_{ij} = || (S_i,\ I_j)||$ and the min by

$ \text{min}_{1 \le i \le n,1 \le j \le n} \{ M_{ij} \}$

Does this help?

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    I'm going with min1≤i≤n,1≤j≤n{||(Si, Ij)||}2010-12-28