# 29 Vectors

Vectors in two-dimensions are made up of an initial point and a terminal point. In the -coordinate plane, the initial point is at (0,0), and the terminal point is at some other coordinate [16]. If we have a vector

then ( is the terminal point, and and are the components [16]. One more important fact is that a vector is denoted with a bold lowercase letter [16]. Vectors do not have to be two-dimensional. In fact, they can have as many dimensions as we want. A vector in -dimensions is denoted as [16].

Two basic operations can be performed on vectors, vector addition and scalar multiplication. Vector addition is done component-wise. That is, for two vectors and in dimensions,

For a vector and scalar , scalar multiplication is defined as

As you can see, these operations are performed in much the same way as matrix addition and scalar multiplication of matrices. This makes sense as matrices are a subset of vectors.

We have a great amount of information to discuss relating to vectors so let’s begin our next section on vector spaces.