Assume that I have a matrix with the form : $B = I + H \in \mathbb{R}^{N \times N} $, where $H$ is a positive semidefinite matrix. And I want to find the inverse of the matrix $B$, which is $B^{-1}$.
At first I decompose the matrix $B$ as $B = I_N + H_1^{T}I_KH_1$, where $H_1 \in \mathbb{R}^{K \times N}$. Then I use the Woodbury matrix identity. But it could not make sense. It goes to the primal problem.
So anyone could help out? Is there any possibility that I could utilize the property of the positive semidefinite matrix? Thanks in advance!