coordinate basis

coordinate basis

[kō′ȯrd·ən·ət ′bā·səs]
(mathematics)
A basis for tensors on a manifold induced by a set of local coordinates.
References in periodicals archive ?
Now the set of linearly independent local directional derivatives [E.sub.i] = [partial derivative]/[partial derivative] [X.sup.i] = [[partial derivative].sup.i] gives the coordinate basis of the locally flat tangent space [T.sup.x](M) at a point x [member of] [C.sup.[infinity]].
Taking a local coordinate basis [[theta].sup.i] = [dx.sup.i], a Pfaffian p-form [omega] is the completely anti-symmetric tensor field
With respect to the local coordinate basis elements [E.sub.i] = [[partial derivative].sub.i] of the tangent space [T.sub.x](M), we see that, astonishingly enough, the anti-symmetric product [A,B] is what defines the Lie (exterior) derivative of B with respect to A.
Full browser ?