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Vectors and Tensors

Vector quantities are written in bold typeface, e.g. , and tensors are written in a bold sans serif typeface, e.g. x . Unit vectors are indicated by a caret placed over the symbol, e.g. is the unit vector parallel to . This convention is extended in the usual fashion so that is the unit vector in the direction of the coordinate x. When two vectors or tensors are written sequentially, as in , it is implied that the tensor or outer product is to be taken. This convention is extended so that means that is to be raised to the kth power with respect to the tensor product. To indicate the square of the length of a vector, the symbol is written in a plain type style, i.e. is a rank two tensor (or dyad), whereas is the square of the length of . Moments of functions are are written with a superscript in parentheses, e.g. . These are lth rank tensor quantities that may also be considered as the Taylor coefficients of the Fourier transform, .



Russell Standish
Thu May 18 11:43:52 EST 1995