## Speaker:

## Time:

## Venue:

- A-212 (STCS Seminar Room)

We show that computing the determinant of an nxn matrix whose entries are themselves 2x2 matrices over a field is as hard as computing the permanent over the field (Extending the recent result of Arvind and Srinivasan [STOC 2010]). On the other hand, surprisingly if one restricts the elements to be dxd upper triangular matrices, then determinant can be computed in poly(n^d) time. Combining this with the decomposition theorem of finite algebras, we get the following dichotomy result: if A is a finite dimensional algebra over a finite field, then the commutativity of A/R(A) determines efficient determinant computation (where R(A) is the radical of A).