Geodesic
The Sherman-Morrison formula and eigenvalues of a special bordered matrix
Acta mathematica Universitatis Comenianae, Tome 74 (2005) no. 2 
G. Trenkler; D. Trenkler. The Sherman-Morrison formula and
eigenvalues of a special bordered matrix. Acta mathematica Universitatis Comenianae, Tome 74 (2005) no. 2. http://geodesic.mathdoc.fr/item/AMUC_2005_74_2_a10/
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     author = {G. Trenkler and D. Trenkler},
     title = {The {Sherman-Morrison} formula and
eigenvalues of a special bordered matrix},
     journal = {Acta mathematica Universitatis Comenianae},
     year = {2005},
     volume = {74},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2005_74_2_a10/}
}
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Voir la notice de l'article provenant de la source Comenius University

The article of Ding and Pye is reconsidered and extended. In contrast to their assertion, we find that the Sherman-Morrison~formula is well suited to prove certain statements about a class of bordered matrices.