Let n nonnegative real numbers λ

1

λ

2

……

λ

n

and A

a positive semidefiniteHermitian matrix A of order n

be given. We present sufficient conditions for the solv-ability of muItiplicative inverse eigenvalue problem（（MH）

for short）; find a nonnega-tive diagonal matrix C such that the matrix CA possesses eigenvalues λ

1

λ

2

···

λ

n

.Wepay more attention to the effects of smaller components of{λ

i

}.In the case n=2

thesufficient conditions are also necessary for（MH）to have solutions.