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On linear maps leaving invariant the copositive/completely positive cones

Sachindranath Jayaraman; Vatsalkumar N. Mer — 2024

Czechoslovak Mathematical Journal

The objective of this manuscript is to investigate the structure of linear maps on the space of real symmetric matrices $𝒮^{n}$ that leave invariant the closed convex cones of copositive and completely positive matrices ( ${COP}_{n}$ and ${CP}_{n}$ ). A description of an invertible linear map on $𝒮^{n}$ such that $L ({CP}_{n}) \subset C P_{n}$ is obtained in terms of semipositive maps over the positive semidefinite cone $𝒮_{+}^{n}$ and the cone of symmetric nonnegative matrices $𝒩_{+}^{n}$ for $n \leq 4$ , with specific calculations for $n = 2$ . Preserver properties of the Lyapunov map $X \mapsto A X + X A^{t}$ , the...

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