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In the simplest case, the matrix inversion Lemma gives an explicit formula of the inverse of a positive-definite matrix A added to a rank-one matrix bbH as follows:(A + bbH )-1 = A-1-A-1 b(1 + bH A-1b)-1bHA-1. It is well known in the literature that this formula is very useful to develop a recursive least-squares algorithm for the recursive identification of linear systems or the design of adaptive...
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