hey guys,

i need help in proving this identity. i've been working on it for 3 days now

some notation:

A is a matrix;

A^T is A transpose;

A^-1 is A inverse;

v is a vector;

v^-1 is v inverse;

v^T is v transpose;

Assume A is a non singular matrix and v is a vector with comparable dimension. Prove:

(A + vv^T)^-1 = A^-1 - [ (A^-1v)(v^TA^-1) / (1 + v^TA^-1v) ]

Need help please. or at least some tips. Thanks!