A vector V in the plane or in space is an arrow: it is determined by its length, denoted V and its direction. Two arrows represent the same vector if they have the same length and are parallel …

We shall begin our discussion by defining what we mean by a vector in three dimensional space, and the rules for the operations of vector addition and multiplication of a vector by a scalar.

Another way to think of a vector is a magnitude and a direction, e.g. a quantity like velocity (“the fighter jet’s velocity is 250 mph north-by-northwest”). In this way of think of it, a vector is a …

Many concepts concerning vectors in Rn can be extended to other mathematical systems. We can think of a vector space in general, as a collection of objects that behave as vectors do in …

Together with matrix addition and multiplication by a scalar, this set is a vector space. Note that an easy way to visualize this is to take the matrix and view it as a vector of length m n. Not all …

vector is a bookkeeping tool to keep track of two pieces of information (typically magnitude and direction) for a physical quantity. Examples are position, force and velocity. The vector has …

For a vector function a(x) the variation can be expressed as the inner product of the difference vector dx and the gradient of the vector a. The latter entity is a dyad.