摘要
对分块实对称正定矩阵A，B，C和D，证明了一个矩阵等式( A ⊙ B ) # ( C ⊙ D ) = ( A # C ) ⊙ ( B # D )，这里A ⊙ B和A # B分别是A与B的Tracy-Singh乘积和几何平均，如果A和B是分块实对称矩阵，则有矩阵不等式 ≥ ，其中是矩阵和的Khatri -Rao乘积。
This paper shows that for the block real symmetric positive definite matrices A，,B，C and D， there exists the equality ( A ⊙ B ) # ( C ⊙ D ) = ( A # C ) ⊙ ( B # D )， where A ⊙ B and A # B are Tracy-Singh product and geometric mean of A and B respectively. If A and B are block real symmetric positive definite matrices, then follows matrix inequelity ≥ ， where is Khatri-Rao product of A and B.
