# A class of sparse matrices whose inverse is also sparse?

In general the inverse of a sparse matrix is dense. A notable (but trivial) exception from that rule are diagonal matrices. Is there any other (broad) class of sparse matrices whose inverse is also sparse?

• Sparse low rank perturbations of diagonal matrices will also have sparse inverses, by the Woodbury formula. – Hans Engler Aug 19 '15 at 15:31
• Good point! In addition, any block-diagonal matrix would also do the trick. Any other classes? – user45893 Aug 19 '15 at 17:18