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A Linear Basis of the Free Akivis Algebra
Journal of Mathematical Sciences, 2019Akivis algebras were introduced in 1976, by \textit{M. A. Akivis} in the paper [Sib. Math. J. 17, 3--8 (1976; Zbl 0337.53018); translation from Sibir. Mat. Zh. 17, 5--11 (1976)]. Let \(F(X)\) be the free nonassociative algebra over a field \(K\) with the set \(X\) of free generators.
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Algebra Colloquium, 2006
Table Algebras (A,B) with distinct non-real basis elements a, b∈ B satisfying [Formula: see text], (m, n∈ ℝ+) are studied in this paper. The two cases where either a is real and b is non-real or a, b are both real were completely classified by Arad and Blau. Here, we study the remaining case where a and b are non-real.
Arad, Zvi, Cohen, Efi
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Table Algebras (A,B) with distinct non-real basis elements a, b∈ B satisfying [Formula: see text], (m, n∈ ℝ+) are studied in this paper. The two cases where either a is real and b is non-real or a, b are both real were completely classified by Arad and Blau. Here, we study the remaining case where a and b are non-real.
Arad, Zvi, Cohen, Efi
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Algebra and Logic, 2013
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Isaev, I. M., Kislitsin, A. V.
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Isaev, I. M., Kislitsin, A. V.
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Journal of Systems Science and Complexity, 2015
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Sun, Yao +3 more
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Sun, Yao +3 more
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Extension theorems for linear lattices with positive algebraic basis
Periodica Mathematica Hungarica, 1975An ordered linear spaceV with positive wedgeK is said to satisfy extension property (E1) if for every subspaceL0 ofV such thatL0 ∩K is reproducing inL0, and every monotone linear functionalf0 defined onL0,f0 has a monotone linear extension to all ofV.
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Communications in Statistics - Simulation and Computation, 1987
A simple linear algebraic algorithm to generate a basis of the null space of a given integral matrix is utilized to present a computer algorithm, which in general, is used to reduce the support size of a given design as in a theorem of FoodyHedayat (Theorem 4.1, 1977), and in particular, it is used to produce a basis for trades.
G.B. Khosrovshahi, E.S. Mahmoodian
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A simple linear algebraic algorithm to generate a basis of the null space of a given integral matrix is utilized to present a computer algorithm, which in general, is used to reduce the support size of a given design as in a theorem of FoodyHedayat (Theorem 4.1, 1977), and in particular, it is used to produce a basis for trades.
G.B. Khosrovshahi, E.S. Mahmoodian
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Atomic Energy, 2017
A linear-algebraic form of the equations of the method of characteristics, which is used to approximate the neutron transport equation, is obtained. It is shown on the basis of the obtained linear-algebraic form that the discrete form of the conjugate equation differs from the algebraically discrete problem constructed by linear-algebraic ...
I. R. Suslov, I. V. Tormyshev
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A linear-algebraic form of the equations of the method of characteristics, which is used to approximate the neutron transport equation, is obtained. It is shown on the basis of the obtained linear-algebraic form that the discrete form of the conjugate equation differs from the algebraically discrete problem constructed by linear-algebraic ...
I. R. Suslov, I. V. Tormyshev
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Topics in Quaternion Linear Algebra
, 2014Quaternions are a number system that has become increasingly useful for representing the rotations of objects in three-dimensional space and has important applications in theoretical and applied mathematics, physics, computer science, and engineering ...
L. Rodman
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Japan Journal of Applied Mathematics, 1986
A generalized doubly stochastic matrix is an \(n\times n\) matrix such that each row and column sum is equal to a given \(x\neq 0\) in a field F, where char (F)\(\nmid n\). \(J_ n\) is the \(n\times n\) matrix such that if e is the unit in F and if n is also used to denote the n-fold sum \(e+e+...+e\), then every entry in \(J_ n\) is \(n^{-1 ...
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A generalized doubly stochastic matrix is an \(n\times n\) matrix such that each row and column sum is equal to a given \(x\neq 0\) in a field F, where char (F)\(\nmid n\). \(J_ n\) is the \(n\times n\) matrix such that if e is the unit in F and if n is also used to denote the n-fold sum \(e+e+...+e\), then every entry in \(J_ n\) is \(n^{-1 ...
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The lived experience of linear algebra: a counter-story about women of color in mathematics
Educational Studies in Mathematics, 2020Aditya P. Adiredja, Michelle Zandieh
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