Lombardi, G.; Rebaudo, R. Diagonal matrices with corrections of rank k. (Italian. English summary) Zbl 0635.15009 Riv. Mat. Univ. Parma, IV. Ser. 12, 147-155 (1986). In the class of bordered diagonal matrices modified by a matrix of rank k, the similar matrix as well as the inverse matrix using the Woodbury formula are found for so-called k-tree matrices. For any such matrix a Sturm sequence for the characteristic equation is given in the special case \(k=1\). Some examples are given. Reviewer: R.Ursianu MSC: 15A21 Canonical forms, reductions, classification 15A09 Theory of matrix inversion and generalized inverses Keywords:bordered diagonal matrices; rank; similar matrix; inverse matrix; Woodbury formula; k-tree matrices; Sturm sequence; characteristic equation PDFBibTeX XMLCite \textit{G. Lombardi} and \textit{R. Rebaudo}, Riv. Mat. Univ. Parma, IV. Ser. 12, 147--155 (1986; Zbl 0635.15009)