摘要
§1引言设C是n阶复数矩阵,记Ck是C的k-项复合矩阵（k=1,2,…,n）,即Ck是一个N阶矩阵,N=（?）,它的元素是由C中的所有k阶子式所组成,足标由C的行标和列标用字典排序决定（见[4],或[5]241—242,或[6]19—20）.记C*是C的共轭转置矩阵,即C*=（?）.C的复合矩阵Ck有如下性质.
In this paper it is shown that if C is an n* n complex matrix and C^(k) is the k-th compound of C, 1≤k≤n, N = ( ? ) and if the eigenvalues of C^(k) are labeled inorder of decreasing magnitude |λ_1(C^(K))|≥λ_2(C^(K)|≥…≥λ_NC^(K)|define the partial trace tr_i^((k)(C)) byThen for two n * n Hermrtian matrices A, B,with equality holds if A, B are commutative or k = n.
