Vector Algebra

Definition of a Vector

A vector might defined as simply as something that follows a set of simple algebraic rules. We need to add geometric structure to such a definition to get something that works well with the data we get from physics experiments.

Geometric Vectors

We can describe a geometric vector as the difference between an initial point and a final point, After that, two properties often used to prove that a vector is a vector are also true:

• If you add a first vector to a second vector you get something that is a third vector.
  • “a sum of vectors is a vector”
• If you multiply a vector by a scalar (for us this will always be a real number or a complex number) you get something that is a vector.
  • “a scaled vector is a vector”