2004
DOI: 10.1007/s00454-004-1090-x
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## Abstract: We study metric properties of the cone of homogeneous nonnegative multivariate polynomials and the cone of sums of powers of linear forms, and the relationship between the two cones. We compute the maximum volume ellipsoid of the natural base of the cone of nonnegative polynomials and the minimum volume ellipsoid of the natural base of the cone of powers of linear forms and compute the coefficients of symmetry of the bases. The multiplication by (x 2 1 + · · · + x 2 n ) m induces an isometric embedding of the…

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