Sherman-Morrison formula

  • Thread starter nikozm
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  • #1

I am trying to derive the Sherman-Morrison formula for the following expression:
a*x*(b*AAH+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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Answers and Replies

  • #2
You need to give more details.

Sherman-Morrison formula deals with the inversion of a rank one perturbation of an invertible matrix ##A##. Assuming that ##A^{-1}## is already computed, the formula gives you simple algebraic expression for the inverse of the perturbation; simple means that it does not involve any other inversions, only (matrix) additions and multiplications.

What do you want here? You should be more specific.
Is your matrix ##A## a "tall" one? What inverse you assume to be known?