Notation
We will use to represent the number of distinct data points, or observations.
Let denote the number of variables that are available for use in making predictions.
We will let represent the value of the th variable for the th observation, where , .
We let denote a matrix whose th element is .That is,
We denote as the th row of . is a vector of length , containing the variable measurements for the th observation. That is,
,+ If we are interested in the columns of , which we will write as . Each is a vector of length , That is,
- If we use these notations, we can write as
The notation denotes the transpose of a matrix or vector. For example, while
We use to denote the th observation of the variable on which we wish to predict. Hence, we write the set of all observations in vector form as
We always denote a vector of length n in lower case bold e.g.
If a vector not of length n will be denoted in lower case normal font, e.g. .
Matrix will be denoted using bold capitals, such as .
Random variables will be denoted using capital normal font, e.g. , regardless of their dimensions.
To indicate that an object is a scalar, we will use the notation . To indicate that it is a vector of length , we will use . We will indicate that an object is a matrix using .
Suppose that and . Then the product of and is denoted . That is, . As an example, consider Then