Length of a vector

Sands, D. E.

doi:10.1107/97809553602060000559

International
Tables for
Crystallography
Volume B
Reciprocal space
Edited by U. Shumeli

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International Tables for Crystallography (2006). Vol. B. ch. 3.1, p. 348 | 1 | 2 |

Section 3.1.3. Length of a vector

D. E. Sands^a ^*

^a Department of Chemistry, University of Kentucky, Chemistry–Physics Building, Lexington, Kentucky 40506-0055, USA
Correspondence e-mail: sands@pop.uky.edu

3.1.3. Length of a vector

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By (3.1.2.1), the scalar product of a vector with itself is $[{\bf v} \cdot {\bf v} = (v)^{2}. \eqno(3.1.3.1)]$ The length of v is, therefore, given by $[v = (v^{i} v\hskip 2pt^{j} g_{ij})^{1/2}. \eqno(3.1.3.2)]$ Computation of lengths in a generalized rectilinear coordinate system is thus simply a matter of evaluating the double summation $[v^{i}v\hskip 2pt^{j}g_{ij}]$ and taking the square root.

References

International Tables for Crystallography (2006). Vol. B. ch. 3.1, p. 348