What are the general algorithms used for diagonalization of large Hermitian matrices and Unitary matrices? ($>5000 \times 5000$)
LAPACK 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.