Pfaffians, hafnians and products of real linear functionals

Details Pfaffians, hafnians and products of real linear functionals Pfaffians, hafnians and products of real linear functionals

2007-04-02

arxiv.org/abs/0704.0028v2

Mathematics

Classical Analysis and ODEs

10 pages

Scientific paper

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 R\'ev\'esz 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).

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