On implementing signature-based Gröbner basis algorithms using linear algebraic routines from M4RI [PDF]
ACM Communications in Computer Algebra, 2015 Grobner bases, proposed by Buchberger in 1965 [5], have been proven to be very useful in many aspects of algebra. Faugere introduced the concept of signatures for polynomials and presented the famous F5 algorithm [9]. Since then, signature-based algorithms have been widely investigated, and several variants of F5 have been presented, including F5C [7],
Yao Sun, Dongdai Lin, Dingkang Wang
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Dynamical Basis Theory: Linear-Algebraic Foundations and Quantum Applications Resolving Kochen-Specker Paradox [PDF]
For praising Yaohushua do I hereby politely correct the misconceptions presented in Kochen-Specker paradoxes and other misunderstandings in quantum mechanics! Defeating errors one misonception at a time~! We present a unified framework for Dynamical Basis Theory (DBT), revolutionizing linear algebra through geometry-aware basis constructions.
Parker Emmerson
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Linear algebraic approach to Gröbner–Shirshov basis theory
Journal of Algebra, 2007 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kang, SJ, Lee, DI, Lee, KH, Park, H
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An Alternative Methodical Approach and Its Effectiveness to Learn Change of Basis Matrices in an Engineering Linear Algebra Class [PDF]
2024 ASEE Annual Conference & Exposition ProceedingsOver the years, students have relied on textbook approaches to learn change of basis matrices. These methodologies often stem from complex abstract concepts, making them difficult for students to comprehend, especially for engineering students who do not have sufficient training for proofs.
Meiqin Li
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Finding a Basis of a Linear System with Pairwise Distinct Discrete Valuations on an Algebraic Curve
Journal of Symbolic Computation, 2000 This is a more complete version, including proofs and examples, of a conference proceedings article by the authors [\textit{R. Matsumoto} and \textit{S. Miura} in: Applied algebra, algebraic algorithms and error correcting codes, 13th Int. Symp., AAECC-13, Honolulu 1999, Proc. Lect. Notes Comput. Sci. 1719, 271-281 (1999; Zbl 0958.14041)].
Ryutaroh Matsumoto, Shinji Miura
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Qubit-Efficient Randomized Quantum Algorithms for Linear Algebra [PDF]
PRX Quantum, 2023 We propose a class of randomized quantum algorithms for the task of sampling from matrix functions, without the use of quantum block encodings or any other coherent oracle access to the matrix elements.
Samson Wang, Sam McArdle, M. Berta
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Inexact iterative numerical linear algebra for neural network-based spectral estimation and rare-event prediction. [PDF]
Journal of Chemical Physics, 2023 Understanding dynamics in complex systems is challenging because there are many degrees of freedom, and those that are most important for describing events of interest are often not obvious.
J. Strahan +4 more
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Near-Optimal Algorithms for Linear Algebra in the Current Matrix Multiplication Time [PDF]
ACM-SIAM Symposium on Discrete Algorithms, 2021 In the numerical linear algebra community, it was suggested that to obtain nearly optimal bounds for various problems such as rank computation, finding a maximal linearly independent subset of columns (a basis), regression, or low-rank approximation, a ...
Nadiia Chepurko +3 more
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Lie algebras of differentiations of linear algebras over a field
Дифференциальная геометрия многообразий фигур, 2021 In this paper, we study a system of linear equations that define the Lie algebra of differentiations DerA of an arbitrary finite-dimensional linear algebra over a field.
A. Ya. Sultanov +2 more
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Қарағанды университетінің хабаршысы. Математика сериясы, 2023 In recent years there has been a great interest in the study of Zinbiel (dual Leibniz) algebras. Let A be Zinbiel algebra over an arbitrary field K and let e1,e2,...,em,... be a linear basis of A. In 2010 A.
D.M. Zhangazinova, A.S. Naurazbekova
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