In the three-dimensional Cartesian coordinate system R3 with coordinates (x, y, z), del is defined in terms of partial derivative operators as
where are the unit vectors in their respective directions. Though this page chiefly treats del in three dimensions, this definition can be generalized to the n-dimensional Euclidean space Rn. In the Cartesian coordinate system with coordinates (x1, x2, ..., xn), del is:
where is the standard basis in this space.
More compactly, using the Einstein summation notation, del is written as
Del can also be expressed in other coordinate systems, see for example del in cylindrical and spherical coordinates.
Read more about this topic: Del
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