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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Three Dimensional Chains and the Classification of the Resulting Collineations
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Paperback. Condition: New. Print on Demand. This book delves into the mathematics of collineations in space, with a specific focus on uncovering their invariant figures and classification. The author, a respected mathematician, presents a systematic approach to the subject, beginning with the fundamental properties of three-chainsā"a crucial concept in the study of collineations. They then proceed to classify the collineations in space based on their invariant three-chains, identifying 19 distinct subtypes within 13 general types. Each subtype is carefully defined and its geometric characteristics are explored. Through this thorough analysis, the book provides valuable insights into the behavior of collineations, offering a deeper understanding of their properties and their significance in the broader field of geometry. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Seller Inventory # 9781527871649_0
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