Given vector a = [a1, a2, a3] and vector b = [b1, b2, b3], the dot product of vector a and vector b, denoted as a · b, is given by:
a · b = a1 * b1 + a2 * b2 + a3 * b3
For example, if a = [2, 5, 6] and b = [4, 3, 2], then the dot product of a and b would be equal to:
a · b = 2*4 + 5*3 + 6*2
a · b = 8 + 15 + 12
a · b = 35
In essence, the dot product is the sum of the products of the corresponding entries in two vectors.
How to Calculate the Dot Product in R
There are two ways to quickly calculate the dot product of two vectors in R:
Method 1: Use %*%
The following code shows how to use the %*% function to calculate the dot product between two vectors in R:
#define vectors a <- c(2, 5, 6) b <- c(4, 3, 2) #calculate dot product between vectors a %*% b [,1] [1,] 35
The dot product turns out to be 35.
Note that this function works for data frame columns as well:
#define data df <- data.frame(a=c(2, 5, 6), b=c(4, 3, 2)) #calculate dot product between columns 'a' and 'b' of data frame df$a %*% df$b [,1] [1,] 35
Method 2: Use the dot() function
We can also calculate the dot product between two vectors by using the dot() function from the pracma library:
library(pracma) #define vectors a <- c(2, 5, 6) b <- c(4, 3, 2) #calculate dot product between vectors dot(a, b)  35
Once again, the dot product between the two vectors turns out to be 35.
The following tutorials explain how to calculate a dot product using other statistical software: