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2. B. S. Perkalskis and J. R. Freeman, “ Examining tensors in the lab: The dielectric permittivity and electrical resistivity of wood,” Am. J. Phys. 66, 816–820 (1998);http://dx.doi.org/10.1119/1.18965
2. B. S. Perkalskis and J. R. Freeman, “ Tensors in the lab—The thermal resistivity of wood,” Am. J. Phys. 67, 452–455 (1999).http://dx.doi.org/10.1119/1.19287
3. T. Levi-Civita, The Absolute Differential Calculus (Calculus of Tensors) (Dover, USA, 1977).
4. J. A. Schouten, Tensor Analysis for Physicists (Dover, USA, 1989).
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7. G. E. Hay, Vector and Tensor Analysis (Dover, USA, 1953).
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17.For example, see P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953);
17. F. W. Byron, Jr. and R. W. Fuller, Mathematics of Classical and Quantum Physics (Dover, USA, 1970).
18.We are also assuming that the readers have been exposed to Cramer's rule for solving linear algebraic equations, i.e., that they have some familiarity with the properties of determinants and the inversion of matrices.
19.For completeness, we should add that multiplication by 1 leaves a vector unchanged.
20.For vectors defined in the complex field, the scalar product would not be commutative.
21.In the context of crystallography, the lattice space and its basis are called the direct space and direct basis, whereas the dual basis and the lattice space thereby generated are called the reciprocal basis and reciprocal lattice; V is the volume of the elementary cell of the direct lattice, whereas its inverse is the volume of the elementary cell of the reciprocal lattice. These concepts in crystallography are of utmost importance: the constructive interference which provides a diffraction spectrum occurs only when the vector differences between the wave vectors of the incident and diffracted x-rays are vectors of the reciprocal space.
22.This is in contrast to the formulation followed here and which, as archaic as it might seem, provides nonetheless a practical tool widely used by the working physicist.
23. B. Schutz, Geometrical Methods of Mathematical Physics (Cambridge U.P., Cambridge, 1980).
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