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?

  • 4
    $\begingroup$ Sparse low rank perturbations of diagonal matrices will also have sparse inverses, by the Woodbury formula. $\endgroup$ – Hans Engler Aug 19 '15 at 15:31
  • $\begingroup$ Good point! In addition, any block-diagonal matrix would also do the trick. Any other classes? $\endgroup$ – user45893 Aug 19 '15 at 17:18

Orthohonal sparse matrices: The inverse is the transposed matrix and hence as sparse as the original one.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.