We define a column n-vector to be an array of n numbers, denoted
The number ai is called the ith component of the vector a. Denote by the set of real numbers and by n the set of column n-vectors with real components. We call n an n-dimensional real vector space. We commonly denote elements of n by lowercase bold letters (e.g., x). The components of x n are denoted x1, …, xn.
We define a row n-vector as
The transpose of a given column vector a is a row vector with corresponding elements, denoted a. For example, if