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In the present paper, we treat the problem of learning averages out of a set of symmetric positive-definite matrices (SPDMs). We discuss a possible learning technique based on the differential geometrical properties of the SPDM-manifold which was recently shown to possess a Lie-group structure under appropriate group definition. We first recall some relevant notions from differential geometry, mainly related to Lie-group theory, and then we propose a scheme of learning averages. Some numerical experiments will serve to illustrate the features of the learnt averages.