On the space of Hermitian matrices measure is defined as a product of all the degrees of freedom of the Hermitian matrix
(1)
Last line is due to
(2)
Every matrix in is in one-to-one correspondence with the vector
(3)
Elements of as a vector can be referred to with a help of double index notation . The inner product on this vector space is as always
(4)
so it is actually
(5)
Unitary conjugation leaves this inner product unchanged
(6)
so it's an orthogonal transformation in . Any orthogonal map in has . Since is connected to the identity, . The bottom line is that Jacobian of coordinate transformation is 1.