- #1
szf654
- 6
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Prove that every divergence free vector field on R^n, n>1 is of the form:
v(x)=SUM dAij/dxi *ej
where Aij(x) is smooth function from R^n to R such that Aij(x)=-Aji(x) i.e. matrix $[Aij(x)]$ is skew symmetric for every vector x.
v(x)=SUM dAij/dxi *ej
where Aij(x) is smooth function from R^n to R such that Aij(x)=-Aji(x) i.e. matrix $[Aij(x)]$ is skew symmetric for every vector x.