An Extension of the Matrix Inversion Lemma
Nariyasu MINAMIDE · SIAM Journal on Algebraic and Discrete Methods · 1985
As an extension of the matrix inversion lemma, the representation of the pseudoinverse of the sum of two matrices of the form $( S + \Phi \Phi^* )$ with S hermitian is considered by a geometric approach introducing orthogonal projections associated with the orthogonal decomposition of the related subspaces. As an example, the pseudoinverse of the matrix $( S + \phi \phi^* )$ with $\phi$ a vector is explicitly calculated.