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!