和与积相等的Hermitian矩阵对的惯性及应用
Inertia of Hermitian matrix pairs whose sum is equal to its product and its applications

针对文献[5]在和与积相等的正定矩阵对的Kantorovich型矩阵不等式证明中所使用的等式是不成立的情况，提出沟通Hermitian矩阵的特征值与惯性关系的方法，得到了和与积相等的Hermitian矩阵对的惯性一般表达式. 不仅证明了文献[5]的矩阵不等式是正确的，而且给出使这类正定(或半正定)矩阵对的通常乘积更精细的矩阵不等式.
As the equality used in the proof of Kantorovich’ inequality in for positive definite Hermitian matrix pairs，whose sum is equal to its product，is defective，this paper mediates the relationship between eigenvalue and inertia of Hermitian matrix，and gives us the general expression for Inertia of Hermitian matrix pairs，whose sum is equal to its product. By applications，it not only proves that Kantorovich’ inequality is correct，but also shows some more precise matrix inequalities for product of this class of positive definite (semi-definite) Hermitian matrix pairs