Zobrazeno 1 - 10
of 99
pro vyhledávání: '"Paparella Pietro"'
Autor:
Johnson, Charles R., Paparella, Pietro
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. Although there are some well-known necessary conditions, a solution to the NI
Externí odkaz:
http://arxiv.org/abs/2409.07682
Autor:
Paparella, Pietro
In this note, it is shown that the nilpotency of submatrices of a certain class of adjacency matrices is equivalent to the Collatz conjecture. Our main result extends the previous work of Alves et al. and clarifies a conjecture made by Cardon and Tuc
Externí odkaz:
http://arxiv.org/abs/2406.08498
Autor:
Clark, Benjamin J., Paparella, Pietro
A recently-established necessary condition for polynomials that preserve the class of entrywise nonnegative matrices of a fixed order is shown to be necessary and sufficient for the class of nonnegative monomial matrices. Along the way, we provide a
Externí odkaz:
http://arxiv.org/abs/2401.01471
The statement of the Karpelevic theorem concerning the location of the eigenvalues of stochastic matrices in the complex plane (known as the Karpelevic region) is long and complicated and his proof methods are, at best, nebulous. Fortunately, an eleg
Externí odkaz:
http://arxiv.org/abs/2309.03849
Autor:
Munger, Devon N., Paparella, Pietro
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 celebrated eigenvalue inequality for matrices whose principal minors are po
Externí odkaz:
http://arxiv.org/abs/2303.12852
In this work, it is shown that if $A$ is an $n$-by-$n$ convexoid matrix (i.e., its field of values coincides with the convex hull of its eigenvalues), then the field of any $(n-1)$-by-$(n-1)$ principal submatrix of $A$ is inscribed in the field of $A
Externí odkaz:
http://arxiv.org/abs/2303.06772
Publikováno v:
In Linear Algebra and Its Applications 1 December 2024 702:46-62
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 relevance and import in the study of the nonnegative inverse eigenvalue p
Externí odkaz:
http://arxiv.org/abs/2110.14111
McDonald and Paparella [Linear Algebra Appl. 498 (2016), 145--159] gave a necessary condition on the structure of Jordan chains of $h$-cyclic matrices. In this work, that necessary condition is shown to be sufficient. As a consequence, we provide a s
Externí odkaz:
http://arxiv.org/abs/2110.09709
Autor:
McDonald, Judith J., Paparella, Pietro
A short and elementary proof is given of a celebrated eigenvalue-perturbation result due to Alfred Brauer.
Externí odkaz:
http://arxiv.org/abs/2110.01376