What are the general algorithms used for diagonalization of large Hermitian matrices and Unitary matrices? (>5000 x 5000$>5000 \times 5000$)
LapackLAPACK seems to diagonalize Hermitian matrices almost 20 times as fast as unitary matrices, and as far as I know, the routines are also different. How is the computational complexity calculated in each case?
If there is a review article which answers my questions please point me in that direction.