Mathematical Research Letters

Volume 15 (2008)

Number 2

Pfaffians, hafnians and products of real linear functionals

Pages: 351 – 358



Péter E. Frenkel (Hungarian Academy of Sciences)


We prove pfaffian and hafnian versions of Lieb’s inequalities on determinants and permanents of positive semi-definite matrices. We use the hafnian inequality to improve the lower bound of Révész and Sarantopoulos on the norm of a product of linear functionals on a real Euclidean space (this subject is sometimes called the `real linear polarization constant' problem).

Published 1 January 2008