Abstract: | By virtue of Frobenius norm ‖A‖ F and Speetral norm ‖A‖ S of matrix A=(a ij )∈C n×n , we make a careful study of the properties of Hermitian matrix's trace, obtaining several conclusions, i.e. Tr( AB)=∑ni=1λ i∑nj=1t ij μ j(λ i,μ j is respectively the eigenvalue of A,B , and t ij is a group of nonnegative real numbers: 0≤t ij ≤1 , and ∑ni=1t ij =1,j=1,2,…,n) ;Tr (AB)≤ Tr (A)‖B‖ S ;Tr (AB) H(AB) ]≤Tr (A HA) max 1≤i≤nλ i] 2(λ i is B′s eigenvalue) and so on. |