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 : 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), clarifying what is possible and what is not, essentially dissolves the doubt.