Positive definite matrix products
摘要
The inequalities (12.1.3) are multiplicative analogues of the sub- and superadditive inequalities 8–9 in Theorem 4.1. Thus, replacing addition (of matrices or of functionals) by composition/multiplication, one obtains the structurally similar inequalities above. However, while addition put no restriction on the matrices A and B, the multiplicative inequalities are only valid for commuting SPD matrices.