element of a given basis of a vector space. Unit vector, a vector in a normed vector space whose norm is 1, or a Euclidean vector of length one. Isotropic vector or null vector, in a vector space with a quadratic form, a non-zero vector for which the form is zero. If a null vector exists, the quadratic form is said an isotropic quadratic form. Vectors in specific vector spaces Column vector, a matrix with only one column. The column vectors with a fixed number of rows form a vector space. Row vector, a matrix with only one row. The row vectors with a fixed number of columns form a vector space. Coordinate vector, the -tuple of the coordinates of a vector on a basis of elements. For a vector space over a field , these -tuples form the vector space (where the operation are pointwise addition and scalar multiplication). Displacement vector, a vector that specifies the change in position of a point relative to a previous position. Displacement vectors belong to the vector space of translations. Position vector of a point, the displacement vector from a reference point (called the origin) to the point. A position vector represents the position of a point in a Euclidean space or an affine space. Velocity vector, the derivative, with respect to time, of the position vector. It does not depend of the choice of the origin, and, thus belongs to the vector space of translations. Pseudovector, also called axial vector Covector, an element of the dual of a vector space. In an inner product space, the inner product defines an isomorphism between the space and its dual, which may make difficult to distinguish a covector from a vector. The distinction becomes apparent when one changes coordinates (non-orthogonally). Tangent vector, an element of the tangent space of a curve, a surface or, more generally, a differential manifold at a given point (these tangent spaces are naturally endowed with a structure of vector space) Normal vector or simply normal, in a Euclidean space or, more generally, in an inner product space, a vector that is perpendicular to a tangent space at a point. Gradient, the coordinates vector of the partial derivatives of a function of several real variables. In a Euclidean space the gradient gives the magnitude and direction of maximum increase of a scalar field. The gradient is a covector that is normal