Abstract
Let E be a vector space and suppose that for every p≧2 the pair \( ({ \otimes ^p}E,\;\mathop \otimes \limits^p ) \) is a tensor product for p copies of E. We extend the definition of ⨂p E to the cases p=1 and p=0 by setting ⨂1 E=E and ⨂0 E=Г. The pair \( (\mathop \otimes \limits^p E,\mathop \otimes \limits^p ) \) is called a p-th tensorial power of E and the elements of \( \mathop \otimes \limits^p \) E are called tensors of degree p over E. A tensor of the form x1⨂ ⋯ ⨂x p , p≧1, and tensors of degree zero are called decomposable.
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© 1967 Springer-Verlag Berlin · Heidelberg
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Greub, W.H. (1967). Tensor algebra. In: Multilinear Algebra. Die Grundlehren der mathematischen Wissenschaften, vol 136. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-00795-2_3
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DOI: https://doi.org/10.1007/978-3-662-00795-2_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-00797-6
Online ISBN: 978-3-662-00795-2
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