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Classical mathematical physics uses various scalar, vector and
tensor notations, depending on
the discipline, but for simplicity and uniformity I
will use matrices operators (differential or physical),
and vectors for the object or outcome of operators. Thus, for example,
a second rank tensor with index range three is represented as a 3x3 matrix.
Similarly, an even higher order tensor such as the elastic stiffness can be written
in matrix form. The matrix representation is a widely accepted tool for
complex mathematical descriptions and seems to give a more pictorial
description of the physical processes. Moreover, besides the ease of
representation, numerical applications benefit from efficient matrix algebra.

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Stanford Exploration Project

1/13/1998