The inertia of the symmetric approximation for low-rank matrices
PublisherTaylor & Francis
Rights accessOpen Access
© 2017 Informa UK Limited, trading as Taylor & Francis Group In many areas of applied linear algebra, it is necessary to work with matrix approximations. A usual situation occurs when a matrix obtained from experimental or simulated data is needed to be approximated by a matrix that lies in a corresponding statistical model and satisfies some specific properties. In this short note, we focus on symmetric and positive-semidefinite approximations and we show that the positive and negative indices of inertia of the symmetric approximation and the rank of the positive-semidefinite approximation are always bounded from above by the rank of the original matrix.
CitationCasanellas, M., Fernández-Sánchez, J., Garrote, M. The inertia of the symmetric approximation for low-rank matrices. "Linear and multilinear algebra", 10 Novembre 2017, vol. 66, núm. 11, p. 2349-2353