How to store a SparseArray?

Question

How to Export/Write a SparseArray?
How to Import/Read a SparseArray?
Is it always stored as a normal array?
How can it be stored in a dense form?
Is a numerical SparseArray different to
Export/Import from a string one?

Answer 1

The two file formats I am familiar with, with respect to sparse matrices, are the Harwell-Boeing format, and the Matrix Market format. I have linked to the docs on how you can Import[]/Export[] matrices in those formats, and you'll do well by reading up on them.

Sparse arrays are very much different from lists. For instance, consider these two representations of the $9\times 9$ identity matrix:

idDense = IdentityMatrix[9];
idSparse = SparseArray[Band[{1, 1}] -> 1, {9, 9}];

For the purposes of Equal[], they're the same:

idSparse == idDense
   True

SameQ[] shows that they aren't:

idSparse === idDense
   False

One can peek at heads to see the difference:

Head /@ {idSparse, idDense}
   {SparseArray, List}

If, for some reason, you need to convert your sparse array to a dense array, that's what Normal[] is for:

Normal[idSparse] === idDense
   True

See the docs for SparseArray[] and Normal[] for more details.