pat_bnd: Pataki bounds

In damelunx/symconivol: A package for curvature measures of symmetric cones

Description

pat_bnd provides the Pataki inequalities for given beta and n.

Usage

pat_bnd(beta, n)

Arguments

beta	Dyson index specifying the underlying (skew-) field: beta==1: real numbers beta==2: complex numbers beta==4: quaternion numbers
n	size of matrix

Value

The output of pat_bnd is a list of five elements:

• d: ambient dimension of corresponding Euclidean space, given in terms of beta,n by n+beta*choose(n,2)

• k_low: function returning the lower bound for index k, given r

• k_upp: function returning the upper bound for index k, given r

• r_low: function returning the lower bound for index r, given k

• r_upp: function returning the upper bound for index r, given k

See also

leigh

Package: symconivol

Examples

# considering the case of 3x3 complex unitary matrices
beta <- 2
n <- 3
P <- pat_bnd(beta,n)

# ambient dimension
P$d

# bounds for index k, given r
P$k_low(0:n)
P$k_upp(0:n)

# bounds for index r, given k
P$r_low(0:P$d)
P$r_upp(0:P$d)

damelunx/symconivol documentation built on May 17, 2019, 7:01 p.m.