23 citations · 110 across the 26 of their papers we have counts for
28 papers
Perron similarities and the nonnegative inverse eigenvalue problem
Charles R. Johnson, Pietro Paparella
The longstanding nonnegative inverse eigenvalue problem (NIEP) is to determine which multisets of complex numbers occur as the spectrum of an entry-wise nonnegative matrix. Althoug…
The converse of the Cowling--Obrechkoff--Thron theorem
Devon N. Munger, Pietro Paparella
In this work, the converse of the Cowling--Obrechkoff--Thron theorem is established. In addition to its theoretical interest, the result fills a gap in the proof of Kellogg's celeb…
Matrices whose field of values is inscribed in a polygon
Matthew J. Fyfe, Yesenia Hernandez, Pietro Paparella +1
In this work, it is shown that if is an -by- convexoid matrix (i.e., its field of values coincides with the convex hull of its eigenvalues), then the field of any …
Kronecker products of Perron similarities
Janelle M. Dockter, Pietro Paparella, Robert L. Perry +1
An invertible matrix is called a Perron similarity if one of its columns and the corresponding row of its inverse are both nonnegative or both nonpositive. Such matrices are of rel…
Jordan chains of -cyclic matrices, II
Andrew L. Nickerson, Pietro Paparella
McDonald and Paparella [Linear Algebra Appl. 498 (2016), 145--159] gave a necessary condition on the structure of Jordan chains of -cyclic matrices. In this work, that necessary…
A short and elementary proof of Brauer's theorem
Judith J. McDonald, Pietro Paparella
A short and elementary proof is given of a celebrated eigenvalue-perturbation result due to Alfred Brauer.
Polynomials that preserve nonnegative matrices of order two
Benjamin J. Clark, Pietro Paparella
A known characterization for entire functions that preserve all nonnegative matrices of order two is shown to characterize polynomials that preserve nonnegative matrices of order t…
Polynomials that preserve nonnegative matrices
Benjamin J. Clark, Pietro Paparella
In further pursuit of a solution to the celebrated nonnegative inverse eigenvalue problem, Loewy and London [Linear and Multilinear Algebra 6 (1978/79), no.~1, 83--90] posed the pr…
Matricial Proofs of Some Classical Results about Critical Point Location
Charles R. Johnson, Pietro Paparella
The Gauss--Lucas and Bôcher--Grace--Marden theorems are classical results in the geometry of polynomials. Proofs of the these results are available in the literature, but the appro…
A proof of the elliptical range theorem via Kippenhahn's theorem
Pietro Paparella, Luis J. Ramirez, Yen-Fen Wang
The elliptical range theorem asserts that the field of values (or numerical range) of a two-by-two matrix with complex entries is an elliptical disk, the foci of which are the eige…
Realizing Suleĭmanova spectra via permutative matrices, II
Pietro Paparella, Amber R. Thrall
In this work, the real nonnegative inverse eigenvalue problem is solved for a particular class of permutative matrix. The necessary and sufficient condition there is also shown to…
On the realizability of the critical points of a realizable list
Sarah L Hoover, Daniel A. McCormick, Pietro Paparella +1
The nonnegative inverse eigenvalue problem (NIEP) is to characterize the spectra of entrywise nonnegative matrices. A finite multiset of complex numbers is called realizable if it…
A Short and Elementary Proof of the Two-sidedness of the Matrix-Inverse
Pietro Paparella
An elementary proof of the two-sidedness of the matrix-inverse is given using only linear independence and the reduced row-echelon form of a matrix. In addition, it is shown that a…
Eisenstein's criterion, Fermat's last theorem, and a conjecture on powerful numbers
Pietro Paparella
Given integers , we define monic polynomials , , and with the property that is a zero of if and only if the triple satisfies…
The NIEP
Charles R. Johnson, Carlos Marijuán, Pietro Paparella +1
The nonnegative inverse eigenvalue problem (NIEP) asks which lists of complex numbers (counting multiplicity) occur as the eigenvalues of some -by- entry-wise nonnegative…
A matricial view of the Karpelevič Theorem
Charles R. Johnson, Pietro Paparella
The question of the exact region in the complex plane of the possible single eigenvalues of all -by- stochastic matrices was raised by Kolmogorov in 1937 and settled by Karpe…
Row Cones, Perron Similarities, and Nonnegative Spectra
C. R. Johnson, Pietro Paparella
In further pursuit of the diagonalizable \emph{real nonnegative inverse eigenvalue problem} (RNIEP), we study the relationship between the \emph{row cone} and th…
Spectrally Perron Polynomials and the Cauchy-Ostrovsky Theorem
Pietro Paparella
In this note, we simplify the statements of theorems attributed to Cauchy and Ostrovsky and give proofs of each theorem via combinatorial and nonnegative matrix theory. We also sho…
The Volume of the Trace-Nonnegative Polytope via the Irwin-Hall Distribution
Pietro Paparella, Gregory K. Taylor
In this work, we find an explicit expression for the volume of the trace nonnegative polytope via a generalization of the Irwin-Hall distribution. This volume is an upper bound for…
Realizing Suleimanova Spectra via Permutative Matrices
Pietro Paparella
A permutative matrix is a square matrix such that every row is a permutation of the first row. A constructive version of a result attributed to Suleimanova is given via permutative…
Perron Spectratopes and the Real Nonnegative Inverse Eigenvalue Problem
Charles R. Johnson, Pietro Paparella
Call an -by- invertible matrix a \emph{Perron similarity} if there is a real non-scalar diagonal matrix such that is entrywise nonnegative. We give two c…
The critical exponent for generalized doubly nonnegative matrices
Xuchen Han, Charles Johnson, Pietro Paparella
It is known that the critical exponent (CE) for conventional, continuous powers of -by- doubly nonnegative (DN) matrices is . Here, we consider the larger class of diago…
Matrix roots of imprimitive irreducible nonnegative matrices
Judith J. McDonald, Pietro Paparella
Using matrix function theory, Perron-Frobenius theory, combinatorial matrix theory, and elementary number theory, we characterize, classify, and describe in terms of the Jordan can…
Jordan chains of -cyclic matrices
Judith J. McDonald, Pietro Paparella
Arising from the classification of the matrix-roots of a nonnegative imprimitive irreducible matrix, we present results concerning the Jordan chains of an -cyclic matrix. We als…