Weak log majorization and determinantal inequalities

Tin-Yau Tam, Pingping Zhang

Denote by ${\P }_n$ the set of $n\times n$ positive definite matrices. Let $D=D_1\oplus \cdots \oplus D_k$, where $D_1\in {\P }_{n_1},\dots ,D_k\in {\P }_{n_k}$ with $n_1+\cdots +n_k=n$. P…