Über die Determinanten mit überwiegender Hauptdiagonale

The Brauer–Ostrowski Theorem for Matrices of Operators

“…In [5] and [1] Ostrowski and Brauer independently observed that each eigenvalue of a matrix A = (a jk ) ∈ C n×n , n ≥ 2 is contained in a Cassini oval   with r = s. In [2] Feingold and Varga obtained the corresponding result for block matrices. In several cases these results lead to a better localization of the spectrum of a matrix than Gershgorin's Theorem, compare [8] and the references given there.…”

Square-free criteria for polynomials using no derivatives

“…A complete bibliography of this theorem is contained in [15]. Other conditions for the nonvanishing of a determinant were obtained by Ostrowski in [10]- [14], using only the moduli of the elements of an n × n complex matrix A = (a ij ) and some simple combinations of these moduli. The results of Ostrowski use essentially the expressions:…”

Schur complement of general H‐matrices

“…The concept of nonsingular M -matrix and H-matrix was introduced by Ostrowski [18] in the study of the convergence of iteration processes and spectral theory. Later, these definitions were extended by Fiedler and Ptak to possible singular M -matrices [8] and H-matrices [9].…”