On the Rotation of a Vector Field in a Four-Dimensional Space

Abstract

Recently I published a paper in the journal ALAMT ( Advances in Linear Algebra & Matrix Theory ) and explored the possibility of obtaining products of vectors in dimensions higher than three [1]. In continuation to this work, it is proposed to develop, through dimensional analogy, a vector field with notation and properties analogous to the curl, in this case applied to the space IR 4 . One can see how the similarities are obvious in relation to the alge braic properties and the geometric structures, if the rotations are compared in spaces of three and four dimen sions.