69 citations · 85 across the 3 of their papers we have counts for
6 papers · 1 filter
Hyperdeterminantal relations among symmetric principal minors
Olga Holtz, Bernd Sturmfels
The principal minors of a symmetric -matrix form a vector of length . We characterize these vectors in terms of algebraic equations derived from the $ 2{\times}2{\…
M-matrices satisfy Newton's inequalities
Olga Holtz
Newton's inequalities are shown to hold for the normalized coefficients of the characteristic polynomial of any - or inverse -matrix. They ar…
Potter, Wielandt, and Drazin on the matrix equation , with some new answers to old questions
Olga Holtz, Volker Mehrmann, Hans Schneider
In this partly historical and partly research oriented note, we display a page of an unpublished mathematical diary of Helmut Wielandt's for 1951. There he gives a new proof of a t…
Applications of the duality method to generalizations of the Jordan canonical form
Olga Holtz
The Jordan normal form for a matrix over an arbitrary field and the canonical form for a pair of matrices under contragredient equivalence are derived using Ptak's duality method.
Theorems and counterexamples on structured matrices
Olga Holtz
The subject of Chapter 1 is GKK -matrices and related topics. Chapter 2 is devoted to boundedly invertible collections of matrices, with applications to operator norms and splin…
Functions preserving nonnegativity of matrices
Gautam Bharali, Olga Holtz
The main goal of this work is to determine which entire functions preserve nonnegativity of matrices of a fixed order -- i.e., to characterize entire functions with the pro…