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In this paper, we develop a novel strategy to compute the transition matrix for the projection problem in a distributed fashion through gossiping in Wireless Sensor Networks. So far, the transition matrix had to be computed off-line by a third party and then provided to the network. The Subspace Projection Problem is useful in various application scenarios (e.g. spectral spatial maps in cognitive radios) and consists of projecting the observed sampled spatial field into a subspace of interest with lower dimension. Although the actual exact computation of the optimal transition matrix is not feasible in a distributed way, we develop an algorithm that is based on well known results from linear algebra and a distributed genetic algorithm in order to compute an approximation of the optimal matrix to a desired precision.