Determinantal inequalities for positive definite matrices

✍ Scribed by Charles R. Johnson; Wayne W. Barrett

• Publisher: Elsevier Science
• Year: 1993
• Tongue: English
• Weight: 609 KB
• Volume: 119
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(93)90119-e

✦ Synopsis

We consider the problem of identifying all determinantal inequalities valid on all positive definite matrices. This is fundamentally a combinatorial problem about relations between collections of index sets. We describe some general structure of this problem and give sufficient and necessary conditions that coincide for collections of no more than 3 index sets each. det A[Ia v p, < det 4~1 det 0'1 ' detA[anP]