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- Arithmetic for closed ballsPublication . Beites, P. D.; Nicolás, A. P.; Vitoria, JoseInspired by circular complex interval arithmetic, an arithmetic for closed balls in Rn is pursued. In this sense, the properties of certain operations on closed balls in Rn, some of which related either to the Hadamard product of vectors or to the 2-fold vector cross product when n ∈ {3, 7}, are studied. In particular, known results for operations on closed balls in C, which can be identified with R2, are extended to closed balls in Rn.
- Vector cross product differential and difference equations in R-3 and in R-7Publication . Beites, P. D.; Nicolás, A. P.; Saraiva, Paulo; Vitoria, JoseThrough a matrix approach of the 2-fold vector cross product in R^3 and in R^7, some vector cross product di erential and di erence equations are studied. Either the classical theory or convenient Drazin inverses, of elements belonging to the class of index 1 matrices, are applied.
- On skew-symmetric matrices related to the vector cross product in R^7Publication . Beites, P. D.; Nicolás, Alejandro; Vitoria, JoseA study of real skew-symmetric matrices of orders 7 and 8, de ned through the vector cross product in R7, is presented. More concretely, results on matrix properties, eigenvalues, (generalized) inverses and rotation matrices are established.
- Eigenvalues of matrices related to the octonionsPublication . Serôdio, Rogério; Beites, P. D.; Vitoria, JoseA pseudo real matrix representation of an octonion, which is based on two real matrix represen- tations of a quaternion, is considered. We study how some operations defined on the octonions change the set of eigenvalues of the matrix obtained if these operations are performed after or before the matrix representation. The established results could be of particular interest to researchers working on estimation algorithms involving such operations.
- Intersection of a Double Cone and a Line in the Split-Quaternions ContextPublication . Serôdio, Rogério; Beites, P. D.; Vitoria, JoseThis is a work on an application of the real split-quaternions to Spatial Analytic Geometry. Concretely, the intersection of a double cone and a line, which can be the empty set, a point, two points or a line, is studied in the real split-quaternions setting.