Results 201 to 210 of about 30,222 (232)

ComRoPE: Scalable and Robust Rotary Position Embedding Parameterized by Trainable Commuting Angle Matrices

Computer Vision and Pattern Recognition
The Transformer architecture has revolutionized various fields since it was proposed, where positional encoding plays an essential role in effectively capturing sequential order and context.
Hao Yu, Tangyu Jiang, Shuning Jia, Shannan Yan, Shunning Liu, Haolong Qian, Guanghao Li, Shuting Dong, Huaisong Zhang, Chun Yuan   +9 more
semanticscholar   +1 more source

Commutators of nilpotent matrices

Linear and Multilinear Algebra, 1976
A matrix of zero trace is, with certain exceptions, the commutator of nilpotent matrices. It may (so far as we know) be necessary to go outside the original field for the entries of the nilpotent matrices.
openaire   +1 more source

Families of Square Commutative 2х2 Matrices

2023
The objective of this study is to define and investigate the families of square matrices of order 2 with a commutative multiplication operation to be used in cryptographic information transformation. The general linear group of order n over the prime field of integers modulo p has been investigated.
Shcherba, Anatoly, Faure, Emil, Skutskyi, Artem, Kharin, Oleksandr   +3 more
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Hamacher Operations on Pythagorean Fuzzy Matrices and Fermatean Fuzzy Matrices

Annals of Pure and Applied Mathematics
This study aims to extend Pythagorean and Fermatean fuzzy matrices within the framework of Hamacher operations. This paper introduces the concepts of Pythagorean fuzzy matrices and Hamacher operations for Fermatean fuzzy matrices and discusses several ...
Debasis Mahata
semanticscholar   +1 more source

Addendum: Commutativity for Systems of (2 × 2) Selfadjoint Matrices

Linear and multilinear algebra, 1993
A purely analytic criterion is presented which characterises the commutativity of a finite-collection of (2x2) selfadjoint matrices. Indeed, it is always possible to associate with such matrices their so called Weyl Calculus which is a matirx-valued ...
B. Jefferies, W. Ricker
semanticscholar   +1 more source

Commutators of Matrices with Prescribed Determinant

Canadian Journal of Mathematics, 1968
Let K be a commutative field, let GL(n, K) be the multiplicative group of all non-singular n × n matrices with elements from K, and let SL(n, K) be the subgroup of GL(n, K) consisting of all matrices in GL(n, K) with determinant one. We denote the determinant of matrix A by |A|, the identity matrix by In, the companion matrix of polynomial p(λ) by C(p ...
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Certain Sets of Anti-Commuting Toeplitz Matrices

Journal of Mathematical Sciences, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +1 more source

On Dominance and Varieties of Commuting Matrices

The Annals of Mathematics, 1961
[4]), a question first raised by Goto. In the same section it is shown that the algebra generated by a pair of commuting n x n matrices can not have dimension greater than n, and that this algebra can always be embedded in a commutative algebra of dimension exactly n, a result derived by introducing the notion of a specialization of an algebra of ...
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The commuting triples of matrices

2012
The irreducibility of the variety C(m,n) commuting m-tuples of n X n matrices has been studied by several authors. It is known that this variety is irreducible if m=2, n=1,2,3 and reducible if m,n>=4. The irreducibility of C(3,n) was asked by Gersteinhaber.
openaire   +1 more source

Commutativity of Matrices Up to a Matrix Factor

Journal of Mathematical Sciences, 2020
N. A. Kolegov, O. Markova
semanticscholar   +1 more source