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is the volume form on <math>M</math>. To define the Hodge star operator for general forms, we simply extend the above definition by linearity.
is the volume form on <math>M</math>. To define the Hodge star operator for general forms, we simply extend the above definition by linearity.
==Example==
Give <math>R^2</math> the standard metric so that <math>dx, dy</math> is a coframe. Then the volume form is <math>dx\wedge dy</math>. Thus,
<math>
*dx = dy
*dy = -dx
</math>
and in general
<math>
* fdx + gdy = fdy - gdx
</math>