In some case the Compile's syntax is quite straightforward. Es. for rank 1  e rank 2 tensors:

    Quiet[Remove[cf]];
    cf = Compile[
       {{x, _Real, 1}}
       , Total[x]
       ];

and

    Quiet[Remove[cf]];
    cf = Compile[
       {{x, _Real, 2}}
       , Inverse[x] (*Inverse isn't compileable: here is used merely as signpost*)

       ];
Or, even, 

    Quiet[Remove[cf]];
    cf = Compile[
       {{x, _Real, 2}, {y, _Real, 2}}
       , Det[x] + Det[y] (*Det isn't compileable: here is used merely as signpost*)
       ];
    cf[matrixA, matrixB]

But what if the arguments are intricated ? What is the syntax needed ? 


A workaround to circumvent this question was proposed [here][1] : *Not the most elegant but could you flatten and join and then "unflatten" and separate afterwards ?*

Please, can you give examples for a function having as argument (all atomic expression are understood Real):

- a matrix of lists
- a matrix of matrices
- a matrix whose element are {x_Real , a matrix }
- a matrix whose element are {x_List , a matrix }
- etc.


**Addendum**

This question has been put on hold, but in IMHO the answer given below (see [Jokeur][2]), clarifying what is possible and what is not, essentially dissolves the doubt.


  [1]: http://mathematica.stackexchange.com/questions/39360/can-i-return-lists-with-different-dimensions-from-a-compiled-function
  [2]: http://mathematica.stackexchange.com/users/38786/jokeur