Zobrazeno 1 - 10
of 92
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
Publikováno v:
Special Matrices, Vol 7, Iss 1, Pp 213-217 (2019)
An elementary proof of a fundamental result on doubly stochastic matrices in Frobenius normal form is given. This result is used to establish several well-known results concerning permutations, including a theorem due to Ruffini.
Externí odkaz:
https://doaj.org/article/bce27277cf044fcfb1cc83108907c856
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
Autor:
Paparella Pietro
Publikováno v:
Special Matrices, Vol 5, Iss 1, Pp 123-126 (2017)
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 show that each simple sufficient condition in each statement is also nece
Externí odkaz:
https://doaj.org/article/eaec88ce83b6457e97d6ffd1ba485224
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