Vector calculus concerns differentiation and integration of vector or scalar fields. This type can be generalized to sequences of elements of some vector space. Here formula 76 is a "K"-dimensional real vector and formula 77 is a scalar parameter. Linear maps are mappings between vector spaces that preserve the vector-space structure. The signal extracted by a weighted vector formula 78 is formula 97. Where formula 25 if the flow velocity vector formula 26. Consider a function formula 20 of a formula 21-dimensional vector . A spherical harmonic depends on the unit vector formula 35. Let formula 18 be a unit vector (the rotation axis) and let formula 19. Also, let denote the maximum norm of an input vector. The curl is a form of differentiation for vector fields. Let X be a "d"-dimensional random vector expressed as column vector. These solutions represent planar waves traveling in the direction of the normal vector . Another example is the curl of a curl of a vector field. There are a number of direct consequences of the vector space axioms.