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(ANTI)COMMUTATIVE ALGEBRAS WITH A MULTIPLICATIVE BASIS
Bulletin of the Australian Mathematical Society, 2014AbstractA basis ${\mathcal{B}}=\{u_{i}\}_{i\in I}$ of a commutative or anticommutative algebra $\mathfrak{C},$ over an arbitrary base field $\mathbb{F}$, is called multiplicative if for any $i,j\in I$ we have that $u_{i}u_{j}\in \mathbb{F}u_{k}$ for some $k\in I$.
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An algebraic hierarchical basis preconditioner
Applied Numerical Mathematics, 1992Consider the solution of linear systems of equations \(Ax=b\) where the coefficient matrix \(A\) satisfies \(A^ T=A\), \(a_{ij}\leq 0\) if \(i\neq j\) and \(\sum_ ja_{ij}=0\) for all \(i\). Such systems arise naturally in electrical resistance networks but also from discretizing partial differential equations.
Guo, Renli, Skeel, Robert D.
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A basis theorem for matrix algebras
Linear and Multilinear Algebra, 1980Let F be a field and let M n(F) denote the algebra of n×n matrices over F. Let P∈Mn (F) be such that its characteristic polynomial is irreducible in F[x]. We show that if Q∈Mn (F) has rank one, then {Pi Qj |⩽i,j⩽n-1} is a basis for Mn (F). (The fact that P,Q generate Mn (F), while being a consequence of this result, is easily established independently;
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A method for determining the canonical basis of an ideal in an algebraic field
Mathematische Annalen, 1931C C Macduffee
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Algebraic Chase Decoding of Elliptic Codes Through Computing the Gröbner Basis
2022Fangguo Zhang, Yunqi Wan
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An orthogonal basis for non-uniform algebraic-trigonometric spline space
Applied Mathematics, 2014Guo-Zhao Wang
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Gröbner basis approach to list decoding of algebraic geometry codes
Applicable Algebra in Engineering, Communications and Computing, 2007Patrick Fitzpatrick
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Algebraic basis of heaviside operational calculus
Journal of the Franklin Institute, 1968openaire +2 more sources