Vectors and matrices

A vector is an object with magnitude and direction (velocity, force, acceleration, etc). A scalar is an object with just magnitude (temperature, pressure, age, length). A vector, denoted ~v or v, has no initial point and is often best thought of as at the origin. A vector may be written in component form ~v = 〈v1, v2, v3〉 (in three dimensions) but it is important to remember that the components are dependent on the coordinate system in use. The vector as a whole is a real object; the components are a tool. One special vector to keep in mind is the zero (or null) vector ~0 whose components are all zero (in every coordinate system).