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Tensor field

Let A be continuously differentiable second-order tensor field defined as follows:

the divergence in cartesian coordinate system is a first-order tensor field and can be defined in two ways:

and

We have

If tensor is symmetric A = A then div (A) = ∇ ⋅ A {\displaystyle \operatorname {div} (\mathbf {A})=\nabla \cdot \mathbf {A} }. Because of this, often in the literature the two definitions (and symbols div and ∇ ⋅ {\displaystyle \nabla \cdot }) are used interchangeably (especially in mechanics equations where tensor symmetry is assumed).

Expressions of ∇ ⋅ A {\displaystyle \nabla \cdot \mathbf {A} } in cylindrical and spherical coordinates are given in the article del in cylindrical and spherical coordinates.