# Diagonalization of Hermitian matrices vs Unitary matrices

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.

• The one who downvoted me, please help me out to find a proper forum to ask this question. I really need a reference. – Roopayan Ghosh Oct 30 at 15:48