Zobrazeno 1 - 10
of 141
pro vyhledávání: '"Plosker, Sarah"'
A matrix is said to have factor width at most $k$ if it can be written as a sum of positive semidefinite matrices that are non-zero only in a single $k \times k$ principal submatrix. We explore the ``factor-width-$k$ rank'' of a matrix, which is the
Externí odkaz:
http://arxiv.org/abs/2405.11556
Autor:
Kim, Sooyeong, Monterde, Hermie, Ahmadi, Bahman, Chan, Ada, Kirkland, Stephen, Plosker, Sarah
An $s$-pair state in a graph is a quantum state of the form $\mathbf{e}_u+s\mathbf{e}_v$, where $u$ and $v$ are vertices in the graph and $s$ is a non-zero complex number. If $s=-1$ (resp., $s=1$), then such a state is called a pair state (resp. plus
Externí odkaz:
http://arxiv.org/abs/2404.16654
Autor:
Johnston, Nathaniel, Plosker, Sarah
Publikováno v:
Linear Algebra and its Applications, 704:309-339, 2025
A graph is called "Laplacian integral" if the eigenvalues of its Laplacian matrix are all integers. We investigate the subset of these graphs whose Laplacian is furthermore diagonalized by a matrix with entries coming from a fixed set, in particular,
Externí odkaz:
http://arxiv.org/abs/2308.15611
Hadamard diagonalizable graphs are undirected graphs for which the corresponding Laplacian is diagonalizable by a Hadamard matrix. Such graphs have been studied in the context of quantum state transfer. Recently, the concept of a weak Hadamard matrix
Externí odkaz:
http://arxiv.org/abs/2307.01859
Publikováno v:
Physical Review A, 106:052417, 2022
We investigate the set of quantum states that can be shown to be $k$-incoherent based only on their eigenvalues (equivalently, we explore which Hermitian matrices can be shown to have small factor width based only on their eigenvalues). In analogy wi
Externí odkaz:
http://arxiv.org/abs/2205.05110
Autor:
Johnston, Nathaniel, Plosker, Sarah
Publikováno v:
In Linear Algebra and Its Applications 1 January 2025 704:309-339
Publikováno v:
J. Algebr. Comb. 58, 623-649 (2023)
Twin vertices in simple unweighted graphs are vertices that have the same neighbours and, in the case of weighted graphs with possible loops, the corresponding incident edges have equal weights. In this paper, we explore the role of twin vertices in
Externí odkaz:
http://arxiv.org/abs/2201.02720
Publikováno v:
Electronic Journal of Linear Algebra, 38:760-776, 2022
We develop numerous results that characterize when a complex Hermitian matrix is Birkhoff-James orthogonal, in the trace norm, to a (Hermitian) positive semidefinite matrix or set of positive semidefinite matrices. For example, we develop a simple-to
Externí odkaz:
http://arxiv.org/abs/2109.05552
Publikováno v:
2020 IEEE CCECE, London, ON, Canada, 2020, pp. 1-4
Decolonization and Indigenous education are at the forefront of Canadian content currently in Academia. Over the last few decades, we have seen some major changes in the way in which we share information. In particular, we have moved into an age of e
Externí odkaz:
http://arxiv.org/abs/2104.04071
Weyl's unitary matrices, which were introduced in Weyl's 1927 paper on group theory and quantum mechanics, are $p\times p$ unitary matrices given by the diagonal matrix whose entries are the $p$-th roots of unity and the cyclic shift matrix. Weyl's u
Externí odkaz:
http://arxiv.org/abs/2101.00129