Householder transformation and some geometric applications

This thesis includes three main parts. The first is dedicated to the introduction which contains the fundamental definitions, concepts and properties. In the second part, in a vector space V with an inner product is being used, some definitions and properties for a reflexion transformation are handled in general; the previous studies on Householder transformation defined in different vector spaces are given place to. The status of the Householder transformation is mentioned accordingly n-dimensioned Euclidean space and n-dimensioned positively defined reel inner product spaces. In a similar way, Lorentzian-Householder transformation and its properties in Minkowski-3 space and the Householder transformation on the generally defined real inner product spaces also referenced under this part. Besides, the Householder transformation in n-dimensioned complex vector space is analized and some circumstances are presented on reflexing the same normed vectors to each other in this part. In the last part, after stating some properties on perplex numbers, the definition and properties of the Householder transformation on the modul of perplex numbers is studied. Moreover, the hybrid numbers which is a newly studied subject in literature, and their properties are examined before presenting the hybrid-Householder transformation.