Applied Mathematics and Mechanics

, Volume 8, Issue 12, pp 1201–1204 | Cite as

The transformation Φ and general Pythagoras' theorem on the linear manifold

  • Gu An-hai


The primary aim of this paper is to describe the transformation function Φω to extend the conclusion of Pythagoras' theorem for “squared length” of any triangle and to study some geometrical significance of its application


Manifold Vector Space Symplectic Manifold Transformation Function Injective Mapping 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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    Gu An-hai, A discussion on Tan's article “Skew-reflection matrix and the generalization of Householder transformation” and transformation function ϕ,Journal of Northeast Institute of Technology, Shenyang, China, 3 (1983), 15–20. (in Chinese)Google Scholar
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    Gu An-hai, The transformation function ϕ and the condition needed for KUR space Having the fixed point,Applied Mathematics and Mechanics,7, 3 (1986), 293–297.MathSciNetCrossRefGoogle Scholar
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    Gruenberg, K.W. and A.J. Weir,Linear Geometry, Springer-Verlag, New York-Heiderberg-Berlin (1977), 2–121.Google Scholar
  4. [4]
    Gu An-hai, On the structure of continua and the mathematical properties of algebraic elastodynamic of a triclinic structural system,Applied Mathematics and Mechanics,8, 10 (1987), 991-1002.MathSciNetGoogle Scholar
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    Deif, Assem S.,Advanced Matrix Theory for Scientists and Engineers, Abcus Press, Tubridge Wells and London, Halsted Press Division, John Wiley and Sons, New York and Toronto (1982), 158.Google Scholar

Copyright information

© SUT 1987

Authors and Affiliations

  • Gu An-hai
    • 1
  1. 1.Zhengzhou Aluminum PlantZhengzhou

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