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I am trying to derive the Sherman-Morrison formula for the following expression:

a*x*(b*AA^{H}+I)^{-1}*y, where a, b are non-negative scalar values. Also, vectors and matrices are represented by lowercase bold typeface and uppercase bold typeface letters, respectively. Also, (.)^{H}and (.)^{-1}are the Hermitian transposition and inverse operation, respectively.

Any help would be useful.

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# Sherman-Morrison formula

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