Three Dimensional Chains and the Classification of the Resulting Collineations in Space (Classic Reprint): Thesis: Thesis (Classic Reprint) - Softcover

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Excerpt from Three Dimensional Chains and the Classification of the Resulting Collineations in Space: Thesis

If, however, the coefficients in the transformation are restricted to real numbers and if two such transformations are regarded as equivalents only if one can be transformed into the other by a transformation with real coefficients the number of types is increased. Thus in the one-dimensional case we have three well known types usually designated by the terms+,hyperbolic, elliptic, and,.parabolic. Here, furthermore, arises the important additional problem as to the conditions under which a collineation with complex coefficients can be transformed into one with real coefficients. In the one - dimensional case again these confiitions are well known: it is necessarv and sufficient that the projective transformation on the complex variable leave a circle in the Argand plane of the complex variable invariant.

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