Sort a vector of vectors of vectors

Question

Let's hope I'm calling it well, I have this vector, or matrix, now I really don't know what it is

{
{{1,0.4,0,0,0,0},{2,0.5,0,0,0,0},{3,0.2,0,0,0,0}},
{{3,0.2,1,5.5686,23.618,1},{2,0.5,0,0,0,0},{1,0.4,0,0,0,0}}
{{2,0.2,0,5.5686,23.618,1},{3,0.5,0,0,0,0},{1,0.4,0,0,0,0}}
}

I want to sort the second level vectors, in a particular manner that the smallest vectors are ordered by their first element, so they all follow the 1,2,3 order in the first element:

{
{{1,0.4,0,0,0,0},{2,0.5,0,0,0,0},{3,0.2,0,0,0,0}},
{{1,0.4,0,0,0,0},{2,0.5,0,0,0,0},{3,0.2,1,5.5686,23.618,1}}
{{1,0.4,0,0,0,0},{2,0.2,0,5.5686,23.618,1},{3,0.5,0,0,0,0}}
}

I was trying different ways, the last one being the following that I found in another question, but it only sorts a common matrix of the type:

 { { }, { } }

But not of the type:

 { { { } , { } } , { { } , { } } }

This is the code:

For[i = 1, i <= Length[BigVector], i++, 
  SortBy[BigVector[[i]], #[[1]] &]];

Answer 1

mat = {{{1, 0.4, 0, 0, 0, 0}, {2, 0.5, 0, 0, 0, 0}, {3, 0.2, 0, 0, 0, 0}},
       {{3, 0.2, 1, 5.5686, 23.618, 1}, {2, 0.5, 0, 0, 0, 0}, {1, 0.4, 0, 0, 0, 0}} , 
       {{2, 0.2, 0, 5.5686, 23.618, 1}, {3, 0.5, 0,  0, 0, 0}, {1, 0.4, 0, 0, 0, 0}}};

You can use

#[[Ordering[#]]] & /@ mat

or

Sort /@ mat

or

Map[Sort, mat] 

all give

(*  { {{1, 0.4, 0, 0, 0, 0}, {2, 0.5, 0, 0, 0, 0}, {3, 0.2, 0, 0, 0,  0}},
      {{1, 0.4, 0, 0, 0, 0}, {2, 0.5, 0, 0, 0, 0}, {3, 0.2, 1, 5.5686, 23.618, 1}}, 
      {{1, 0.4, 0, 0, 0, 0}, {2, 0.2, 0, 5.5686,  23.618, 1}, {3, 0.5, 0, 0, 0, 0}}} *)