This is an example postgres extension that shows how to implement an "expanded" data type in C as described in this documentation:
"Another feature that's enabled by TOAST support is the possibility of having an expanded in-memory data representation that is more convenient to work with than the format that is stored on disk. The regular or “flat” varlena storage format is ultimately just a blob of bytes; it cannot for example contain pointers, since it may get copied to other locations in memory. For complex data types, the flat format may be quite expensive to work with, so PostgreSQL provides a way to “expand” the flat format into a representation that is more suited to computation, and then pass that format in-memory between functions of the data type."
This repository provides a simple, compilable and runnable example expanded data type that can be used as a basis for other extensions. By way of trivial example, it shows how to expand and flatten a sparse matrix stored in a simple coordinate format.
This isn't meant to be a useful matrix type! It is intentionally simple and inefficient and for illustration purposes only. If you want efficient sparse matrix multiplication I suggest you check out SuiteSparse:GraphBLAS.