15 papers · ranked by Valyu relevance
Changqing Xu
The commutation matrix was first introduced in statistics as a transposition matrix by Murnaghan in 1938. In this paper, we first investigate the commutation matrix which is employed to transform a matrix into its transpose. We then extend the concept of the commutation matrix to commutation tensor and use the…
Madeleine Elyze, Alexander Guterman, Ralph Morrison, Klemen Šivic
> Abstract. The commuting variety of matrices over a given field is a well-studied object in linear algebra and algebraic geometry. As a set, it consists of all pairs of square matrices with entries in that field that commute with one another. In this paper we generalise the commuting variety by using the commuting…
R. P. Nordgren
We present a matrix version of a known method of constructing common eigenvectors of two diagonalizable commuting matrices, thus enabling their simultaneous diagonalization. The matrices may have simple eigenvalues of multiplicity greater than one. The singular value decomposition (SVD) of a class of commuting matrices…
Pascal Koiran
A tuple (Z1, . . . , Zp) of matrices of size r is said to be a commuting extension of a tuple (A1, . . . , Ap) of matrices of size n < r if the Zi pairwise commute and each Ai sits in the upper left corner of a block decomposition of Zi . This notion was discovered and rediscovered in several contexts including…
Haoze He, Daniel Kressner, Bor Plestenjak
It is well known that a family of ${n}\times{n}$ commuting matrices can be simultaneously triangularized by a unitary similarity transformation. The diagonal entries of the triangular matrices define the n joint eigenvalues of the family. In this work, we consider the task of numerically computing approximations to…
Caden Young
Let $M_n$ be an $n\times n$ random matrix whose entries are independent Rademacher random variables, and put $N=\binom n2$. We prove [ Pr(M_nM_n^T=M_n^TM_n)=2^{-N+O(n)}. ] This gives the sharp exponential order for the probability that a random sign matrix is normal. The lower bound is supplied by symmetric sign…
Marco Mamei, Nicola Bicocchi, Marco Lippi, Stefano Mariani + 1 more
'Franco Zambonelli'] Understanding and correctly modeling urban mobility is a crucial issue for the development of smart cities. The estimation of individual trips from mobile phone positioning data (i.e., call detail records (CDR)) can naturally support urban and transport studies as well as marketing applications.…
Daniel Nichol, Peter Jeavons, Alexander G. Fletcher, Robert A. Bonomo + 5 more
In a time when we receive almost daily warnings of a ‘post-antibiotic era’ from the CDC and other groups, and drug development is stalling, we find ourselves in desperate need for novel strategies in the fight against bacterial evolution. Herein, we abstract the process of evolution on a fitness landscape to a Markov…
Markus Pettersen, Nicolai Haug, Joakim Bergli, Thomas M. Surowiec + 1 more
A fundamental challenge in neuroscience and AI is understanding how physical space is mapped into neural representations. While artificial neural networks can generate brain-like spatial representations, such as place and grid cells, their “black-box” nature makes it difficult to determine if these representations…
Dimitrinka Vladeva
In all considered semirings S we assume that there exist a zero element 0 ∈ S such that a + 0 = a and a · 0 = 0 · a = 0 for any a ∈ S and identity element 1 ∈ S such that 1 · a = a · 1 = a for any a ∈ S.
John Urschel, Cristina H Amon
We prove that every element of the special linear group can be represented as the product of at most six block unitriangular matrices, and that there exist matrices for which six products are necessary, independent of indexing. We present an analogous result for the general linear group. These results serve as general…
Alkiviadis G. Akritas, Gennadi Malaschonok
The best method for computing the adjoint matrix of an order n matrix in an arbitrary commutative ring requires O(n β+1/3 log n log log n) operations, provided the complexity of the algorithm for multiplying two matrices is γnβ + o(n β ). For a commutative domain – and under the same assumptions – the complexity of the…
Robert Christian Subroto
Circulant Column Parity Mixers (CCPMs) are a particular type of linear maps, used as the mixing layer in permutation-based cryptographic primitives like Keccak-f (SHA3) and Xoodoo. Although being successfully applied, not much is known regarding their algebraic properties. They are limited to invertibility of CCPMs…
Authors not listed
This paper investigates several chemical systems through the lens of hyperstructures and superhyperstructures. We first review Chemical HyperStructures and Chemical SuperHyperStructures defined by redox-driven hyperoperations on species sets with maximal electromotive force selection. Building on the general (m,n)-…
Lionel Zoubritzky, François-Xavier Coudert
We present here an open-source Julia library for the topological identification of crystalline materials, with algorithmic and computational improvements over the previously available software in the field, resulting in a speed increase of one order of magnitude. This new algorithm and implementation can therefore be…