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hence
 For
we have
that
.
 How does rotating the basis affect coefficients of
vector
a?
Observe that vector coefficients do not transform the
same way as basis vectors. They transform like basis forms,
i.e., ``in the opposite direction'' to the basis vectors.
For this reason upper index objects are often called
contravariant vectors.
 How does rotating the basis affect coefficients
of a form?
Form coefficients, as you see, transform like basis vectors.
For this reason lower index objects are often called
covariant vectors.
 Now consider a tensor
F:
This formula merely confirms what we have already
learnt about forms and vectors.
Next: The Eigensolution and its
Up: The Eigenvalue Problem
Previous: The Eigenvalue Problem
Zdzislaw Meglicki
20010226