An elementary proof of Chollet’s permanent conjecture for 4 × 4 real matrices

Abstract

A proof of the statement per(A ∘ B) ≤ per(A)per(B) is given for 4 × 4 positive semidefinite real matrices. The proof uses only elementary linear algebra and a rather lengthy series of simple inequalities.

Keywords

• chollet conjecture
• positive semidefinite matrices
• hadamard product
• matrix permanent
• 15a15
• 15b48