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Definition
Authier, A., International Tables for Crystallography (2013). Vol. D, Section 1.1.3.7.1, p. [ doi:10.1107/97809553602060000900 ]
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Generalization
Authier, A., International Tables for Crystallography (2013). Vol. D, Section 1.1.3.8.2, p. [ doi:10.1107/97809553602060000900 ]
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Properties of the vector product
Authier, A., International Tables for Crystallography (2013). Vol. D, Section 1.1.3.7.3, p. [ doi:10.1107/97809553602060000900 ]
to the properties of tensors Expression (1.1.3.4) of the vector product shows that it is of a covariant nature. This is indeed correct, and it is well known that the vector product of two vectors of the direct lattice is a vector ...

Vector product
Authier, A., International Tables for Crystallography (2013). Vol. D, Section 1.1.3.7.2, p. [ doi:10.1107/97809553602060000900 ]
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How to change the variance of the components of a tensor
Authier, A., International Tables for Crystallography (2013). Vol. D, Section 1.1.3.6.2, p. [ doi:10.1107/97809553602060000900 ]
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Representation surfaces of second-rank tensors
Authier, A., International Tables for Crystallography (2013). Vol. D, Section 1.1.3.5.2, p. [ doi:10.1107/97809553602060000900 ]
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Tensor nature of physical quantities
Authier, A., International Tables for Crystallography (2013). Vol. D, Section 1.1.3.4, p. [ doi:10.1107/97809553602060000900 ]
a change of basis. The set of nine quantities constitutes therefore the set of components of a tensor of rank 2. Expression (1.1.3.3) is the contracted product of by . A similar demonstration may be used to show the tensor nature ...

Tensor nature of the metric tensor
Authier, A., International Tables for Crystallography (2013). Vol. D, Section 1.1.3.6.1, p. [ doi:10.1107/97809553602060000900 ]
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Multiplication by a scalar
Authier, A., International Tables for Crystallography (2013). Vol. D, Section 1.1.3.3.2, p. [ doi:10.1107/97809553602060000900 ]
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Definition of a tensor
Authier, A., International Tables for Crystallography (2013). Vol. D, Section 1.1.3.1, p. [ doi:10.1107/97809553602060000900 ]
to the properties of tensors For the mathematical definition of tensors, the reader may consult, for instance, Lichnerowicz (1947), Schwartz (1975) or Sands (1995) . 1.1.3.1.1. Linear forms | top | pdf ...

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