# Sherman-Morrison formula

1. Feb 5, 2015

### nikozm

Hi,

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.

Last edited: Feb 5, 2015
2. Feb 6, 2015

### Hawkeye18

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?