pure function - Subtracting elements in a nested list

I have a list containing 500 rows, each of 37 elements; i.e., a 500 x 37 matrix.

My goal is to substract in each row each element from the first. My approach in mind is to call each list by a PureFunction and then to subtract the second element from the first, then the third from the first so in the end I would have a list with 500 sublists, each with 36 elements. I failed to figure out how to call single elements if, as in my case, the the list is called by a PureFunction. I also tried to work with slots, again failing to call the single elements of the already called list. I highly appreciat any help or comments!

Answer

If mat is your matrix, the following should be fast:

mat . SparseArray[
    {{1,_} -> 1, Band[{2,1}] -> -1},
    Dimensions[mat][[2]]+{0,-1}
]

Addendum

Here is a brief speed comparison of the 4 suggested methods:

wreach[m_] := m[[All, 1]] - m[[All, 2 ;;]]
carl[m_] := m . SparseArray[
    {{1, _} -> 1, Band[{2, 1}] -> -1}, 
    Dimensions[m][[2]] + {0, -1}
]
goldberg[m_] := #1 - {##2} & @@@ m
tom[m_] := #[[1]] - #[[2 ;;]] & /@ m

A sample matrix:

mat = RandomReal[10^6, {10^5, 30}];

Speed comparison:

r1 = carl[mat]; // AbsoluteTiming
r2 = wreach[mat]; // AbsoluteTiming
r3 = goldberg[mat]; // AbsoluteTiming
r4 = tom[mat]; // AbsoluteTiming
r1 === r2 === r3 === r4

{0.013968, Null}

{0.029711, Null}

{1.4249, Null}

{0.346468, Null}

True