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 (see figure …

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 directed arrow …

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 Rn. The objects …

The two properties of vector addition that are described by Theorem 1.1.1 are called commutativity and associativity, respectively, and they basically say that we can unambiguously talk about the sum of …

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.

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 purpose of this document is to help you learn to take derivatives of vectors, matrices, and higher order tensors (arrays with three dimensions or more), and to help you take derivatives with respect to …