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data[1,2] = 1.234
print(data[1,2])  -- returns 1.234

Can someone point me to the right resources so I can start reading and testing myself? Or perhaps someone can give me a hint.

You might want to take a look at Numerical Lua.  It uses the syntax:

  local m = matrix(n,n)
  for i = 1, n do m[1][i] = 1 end

Don't know its storage model (Lua or C), but it might give some ideas by looking through the source.