# Spectrahedron-class: An R class to represent a Spectrahedron In volesti: Volume Approximation and Sampling of Convex Polytopes

## Description

A spectrahedron is a convex body defined by a linear matrix inequality of the form A_0 + x_1 A_1 + ... + x_n A_n \preceq 0. The matrices A_i are symmetric m \times m real matrices and \preceq 0 denoted negative semidefiniteness.

## Details

matrices

A List that contains the matrices A_0, A_1, ..., A_n.

## Examples

 1 2 3 4 5 6 A0 = matrix(c(-1,0,0,0,-2,1,0,1,-2), nrow=3, ncol=3, byrow = TRUE) A1 = matrix(c(-1,0,0,0,0,1,0,1,0), nrow=3, ncol=3, byrow = TRUE) A2 = matrix(c(0,0,-1,0,0,0,-1,0,0), nrow=3, ncol=3, byrow = TRUE) lmi = list(A0, A1, A2) S = Spectrahedron(matrices = lmi); 

volesti documentation built on July 14, 2021, 5:11 p.m.