On linear algebra of r-Hankel and r-Toeplitz matrices with geometric sequence
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DOI: 10.1007/s12190-024-02151-y
Abstract: Matrix theory plays a crucial role in solving practical problems and performing computational operations. In particular, specific types of matrices and their linear algebraic properties are of paramount significance for these processes. In this paper,… read more here.
Keywords: algebra; hankel toeplitz; matrices geometric; algebra hankel ... See more keywords
Corrigendum to “Expressing infinite matrices over rings as products of involutions” [Linear Algebra Appl. 532 (2017) 257-265]
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DOI: 10.1016/j.laa.2019.11.013
Abstract: Abstract There is an error in the proof of Theorem 2.3 of [1] . In this corrigendum Theorem 2.3 is rewritten and Theorem 2.5 and Theorem 1.1 of [1] are reproved. read more here.
Keywords: infinite matrices; rings products; expressing infinite; matrices rings ... See more keywords
Corrigendum to: “ On sequences of Toeplitz matrices over finite fields” [Linear Algebra Appl. 561 (2019) 63–80]
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DOI: 10.1016/j.laa.2020.01.008
Abstract: Abstract For each non-negative integer n let A n be an n + 1 by n + 1 Toeplitz matrix over a finite field, F, and suppose for each n that A n is embedded… read more here.
Keywords: matrices finite; toeplitz matrices; sequences toeplitz; finite fields ... See more keywords
Corrigendum to “Representations of ⁎-semigroups associated to invariant kernels with values adjointable operators” [Linear Algebra Appl. 486 (2015) 361–388]
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DOI: 10.1016/j.laa.2020.01.009
Abstract: Abstract We correct a lemma by adding the assumption that the ordered ⁎-space is Archimedean and show by counter-examples and examples that this is needed. read more here.
Keywords: semigroups associated; representations semigroups; associated invariant; invariant kernels ... See more keywords
Corrigendum to “An extension of Haagerup-Harpe inequality” [Linear Algebra Appl. 577 (2019) 69–77]
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DOI: 10.1016/j.laa.2020.04.026
Abstract: Abstract A revised version of the main theorem in A. M. Hamedani et al. (2019) [1] is presented. We prove that for every matrix A ∈ M n which is unitarily similar to a non-negative… read more here.
Keywords: extension haagerup; corrigendum extension; haagerup harpe; inequality ... See more keywords
Variational algorithms for linear algebra
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DOI: 10.1016/j.scib.2021.06.023
Abstract: Quantum algorithms have been developed for efficiently solving linear algebra tasks. However they generally require deep circuits and therefore universal fault-tolerant quantum computers. In this work, we propose variational algorithms for linear algebra tasks that… read more here.
Keywords: algorithms linear; variational algorithms; quantum; algorithms ... See more keywords
Curve Fitting, Linear Algebra, and Solver in an Analytical Chemistry Course: A Facile and Safe Activity Suitable for the Classroom Setting
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DOI: 10.1021/acs.jchemed.9b00421
Abstract: Undergraduate analytical chemistry courses emphasize fundamental stoichiometric and physicochemical analytical techniques with statistical analysis and linear calibrations. Higher-level data analys... read more here.
Keywords: curve fitting; algebra solver; chemistry; analytical chemistry ... See more keywords
Greek ladders via linear algebra
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DOI: 10.1080/0020739x.2018.1440326
Abstract: ABSTRACT Theon's ladder is an ancient method for easily approximating nth roots of a real number k. Previous work in this area has focused on modifying Theon's ladder to approximate roots of quadratic polynomials. We… read more here.
Keywords: via linear; linear algebra; greek ladders; ladders via ... See more keywords
Engaging Activities for Teaching Linear Algebra
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DOI: 10.1080/10511970.2024.2310244
Abstract: ABSTRACT This paper discusses several linear algebra activities designed to help enhance students' skills in collaborating, exploring mathematics, and linking together abstract and visual ways of approaching mathematics. Most of these activities are short, accessible,… read more here.
Keywords: algebra; engaging activities; activities teaching; mathematics ... See more keywords
Determining Feynman Integrals with Only Input from Linear Algebra.
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DOI: 10.1103/physrevlett.129.222001
Abstract: We find that all Feynman integrals (FIs), having any number of loops, can be completely determined once linear relations between FIs are provided. Therefore, FI computation is conceptually changed to a linear algebraic problem. Examples… read more here.
Keywords: input linear; determining feynman; feynman integrals; integrals input ... See more keywords
A Case for Malleable Thread-Level Linear Algebra Libraries: The LU Factorization With Partial Pivoting
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DOI: 10.1109/access.2019.2895541
Abstract: We propose two novel techniques for overcoming load-imbalance encountered when implementing so-called look-ahead mechanisms in relevant dense matrix factorizations for the solution of linear systems. Both techniques target the scenario where two thread teams are… read more here.
Keywords: malleable thread; factorization partial; task; linear algebra ... See more keywords