Get the common lowest values of 2 datasets?

I have 2 datasets,

 a = [ 6.7082    5.3852    3.0000    4.1231    3.1623    7.0711    4.0000    1.0000    1.0000    5.0990    4.4721];
 b = [70.0000   75.0000   49.0000    9.0000   65.0000   79.0000    6.0000   51.0000   56.0000    9.0000   71.0000];

If I was to get the smallest value of each set, how do I get the optimal smallest common value for both sets. eg smallest value of "a" is 1.0000 and smallest value of b is 6.0000, however the corresponding value at the 1.0000 (at same index) is 51.00000 and for 6.0000 you have 4.0000. Maybe this isn't possible to do so but I was wondering can you?

[Joachim Schlosser]

Sounds like a maths homework exercise, doesn't it?

[Ronan]

It isn't homework. I m not sure if I m missing something obvious or if its too abstract to answer. I thought about getting the max and min of both and comparing there percentage but doesn't seem ideal.

[Stephen23]

The arrays a and b do not seem to share any values at all, so how can they have a "common minimum value"? What do you mean by "common value", if this is not the usual meaning of a value that is common to both vectors?

[Adam Barber]

If I understand correctly, you really just want the smallest total column? If so, can't you just add a and b and take the minimum?

[Ronan]

I probably worded it wrongly in saying common value. Because the two datasets are not related the question is out of context. I was trying to relate them so that you could choose which row has the idealistic lowest value. Adding them and taking the minimum is probably the best I can do. It was more of a thought experiment than anything.

Answer 1

[Thorsten]

 [~, idx] = min(a);
 min1 = [a(idx) b(idx)]
 [~, idx] = min(b); 
 min2 = [a(idx) b(idx)]