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Algebra Universalis, 2002
The collection of all \(n\times n\) matrices with entries from a given relation algebra \(\mathcal R\) forms a relation algebra \(M_n(\mathcal R)\) with naturally defined operations. The paper contains lists of properties of \(\mathcal R\) (e.g.\ atomicity, simplicity, representability, non-embeddability, density, etc.) which are preserved also in ...
el Bachraoui, M., van de Vel, M.L.J.
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The collection of all \(n\times n\) matrices with entries from a given relation algebra \(\mathcal R\) forms a relation algebra \(M_n(\mathcal R)\) with naturally defined operations. The paper contains lists of properties of \(\mathcal R\) (e.g.\ atomicity, simplicity, representability, non-embeddability, density, etc.) which are preserved also in ...
el Bachraoui, M., van de Vel, M.L.J.
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2021
This chapter shows how matrix algebra can help overcome the problems in solving a set of three or more simultaneous equations and how it makes it possible to handle large sets of simultaneous linear equations. It concludes by illustrating the applications of matrix algebra.
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This chapter shows how matrix algebra can help overcome the problems in solving a set of three or more simultaneous equations and how it makes it possible to handle large sets of simultaneous linear equations. It concludes by illustrating the applications of matrix algebra.
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Matrix Algebras and Displacement Decompositions [PDF]
SIAM Journal on Matrix Analysis and Applications, 2000 This paper investigates classes of complex \(n\times n\) matrices for which there are formulae enabling computation of a matrix vector product \(Af\) by means of a small number of fast discrete transforms. The basic formula is the ``displacement formula'': \(A=\sum_{m=1}^{\alpha}L_{m}U_{m}\) where \(L_{m}\) and \(U_{m}\) are lower and upper triangular ...
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Matrix Isomorphism of Matrix Lie Algebras
2012 IEEE 27th Conference on Computational Complexity, 2012We study the problem of matrix isomorphism of matrix Lie algebras (MatIsoLie). Lie algebras arise centrally in areas as diverse as differential equations, particle physics, group theory, and the Mulmuley -- Sohoni Geometric Complexity Theory program. A matrix Lie algebra is a set L of matrices that is closed under linear combinations and the operation [
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1996
We will present in this chapter some aspects of matrix algebra that are needed in this book. Most results presented here can be found in standard books on matrix algebra. Proofs are provided for those results that are either easily derived or not readily available elsewhere. For readers who have no knowledge of matrix algebra, this chapter is essential
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We will present in this chapter some aspects of matrix algebra that are needed in this book. Most results presented here can be found in standard books on matrix algebra. Proofs are provided for those results that are either easily derived or not readily available elsewhere. For readers who have no knowledge of matrix algebra, this chapter is essential
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Rota–Baxter operators of nonzero weight on the matrix algebra of order three
Linear and Multilinear Algebra, 2022Maxim Goncharov, Vsevolod Gubarev
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Unital decompositions of the matrix algebra of order three
Communications in Algebra, 2021Vsevolod Gubarev
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