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An Introduction to Tensors

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Part of the book series: Mathematics and Visualization ((MATHVISUAL))

Abstract

This chapter is a short introduction into tensor fields, some basic techniques from linear algebra, differential geometry and the mathematical concept of tensor fields are presented. The main goal of this chapter is to give readers from different backgrounds some fundamentals to access the research papers in the following chapters.

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References

  1. Fuhrmann, P.A.: A Polynomial Approach to Linear Algebra. Springer, Berlin (2002)

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  2. do Carmo, M.P.: Differential Geometry of Curves and Surfaces. Prentice-Hall, Englewood Cliffs, N.J. (1976)

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  3. Spivak, M.: Differential Geometry. Publish or Perish, Berkeley (1979)

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  4. Borisenko, A.I., Tarpov, I.E.: Vector and Tensor Analysis with Applications. Dover, New York (1980)

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  5. Abraham, R., Marsden, J.E., and Ratiu, T.S.: Manifolds, Tensor Analysis, and Applications, 2nd ed. Springer, New York (1991)

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© 2006 Springer-Verlag Berlin Heidelberg

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Hagen, H., Garth, C. (2006). An Introduction to Tensors. In: Weickert, J., Hagen, H. (eds) Visualization and Processing of Tensor Fields. Mathematics and Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-31272-2_1

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