On the Spectrum and Pseudoinverse of a Special Bordered Matrix
The characteristic polynomial of a low rank bordered matrix of special structure is determined by elementary means. This result includes as a special case formula (13) in [A. Farkas, P. Rozsa. Data perturbations of matrices of pairwise comparisons, preprint, 2000] obtained there by the Sherman-Morrison formula. Another application is a simple formula for the pseudoinverse of these bordered matrices. (C) 2001 Elsevier Science Inc. All rights reserved.
Linear Algebra and Its Applications
Pye, W. C.
(2001). On the Spectrum and Pseudoinverse of a Special Bordered Matrix. Linear Algebra and Its Applications, 331(1-3), 11-20.
Available at: https://aquila.usm.edu/fac_pubs/3856