Abstract
In this chapter, we show that tensors can be identified with mathematical AQ1 operators that transform elements from one abstract vector space to another. This viewpoint on tensors is apparently different from those presented in Chaps. 18 and 19, where tensors have been identified as sets of index quantities subject to a transformation law under changes of coordinate systems. However, the viewpoint presented here turns out to be consistent with those presented in the previous two chapters when we introduce the concept of inner product into the abstract vector space (Sect. 20.3.4).
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© 2009 Springer-Verlag Berlin Heidelberg
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Shima, H., Nakayama, T. (2009). Tensor as Mapping. In: Higher Mathematics for Physics and Engineering. Springer, Berlin, Heidelberg. https://doi.org/10.1007/b138494_20
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DOI: https://doi.org/10.1007/b138494_20
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-87863-6
Online ISBN: 978-3-540-87864-3
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