Condition number of a convex cone

The concept of condition number of an invertible matrix plays a fundamental role in numerical linear algebra. This work introduces and studies two condition numbers for closed convex cones in a given Euclidean space. Let K be a closed convex cone that is pointed and solid. The opening-angle condition number \(\Upsilon (K)\) $\mathrm{{\rm Y}}(K)$ is defined as the ratio of both extreme values of the opening angle function of K, whereas the spectral condition number \(\Theta (K)\) $\mathrm{\Theta }(K)$ is defined as the ratio of both extreme critical angles of K.