Lyapunov diagonal semistability of real H-matrices
Let \(A\) be an \(n\times n\) matrix and define the comparison matrix \(B=M(A)\) by \(b_{jj}= \vert a_{jj}\vert\) and \(b_{jk}= - \vert a_{jk}\vert\), \(j\neq k\). Then \(A\) is an H-matrix if \(M(A)\) is an M-matrix. The authors characterize diagonally stable real H-matrices and those real H-matrices which are diagonally semistable but not diagonally stable. The results are applied to a study of the numerical abscissa of real matrices. The work is given in terms of properties of principal submatrices and uses results on determinants due to A. Ostrowski.
scientific article; zbMATH DE number 3922880
scientific article