Nowadays most functions are able to work on sparse matrices and output sparse matrices. If you want to be sure that it is working, use ISSPARSE to check on a small case study, e.g.
>> A = sparse([2 0 3; 4 5 0; 0 0 6]) ;
>> B = sparse([0 1 0; 2 0 2; 3 3 0]) ;
>> C = kron(A, B) ;
>> issparse(C)
ans =
1
>> C = blkdiag(A, B) ;
>> issparse(C)
ans =
1
There is no advantage in using SPARSE on a matrix that is already sparse.
Note that the situation where you convert a dense version of a large matrix to sparse can/should rarely happen. You generally have to build the matrix directly as a sparse matrix, using a call like
S = sparse(I, J, V, m, n) ;
where I and J are vectors of respectively row and column indices, V is a vector of values, and m and n define the size.
One of the rare cases where you transform a dense matrix to sparse is when you build a small matrix that must be used as a basis for building a larger one, which seems to be your case.
