Page 39 - Applied Statistics with R

3.2. DATA STRUCTURES 39

as.matrix(a_vec)

## [,1]
## [1,] 1
## [2,] 2
## [3,] 3

If we use the %*% operator on matrices, %*% again performs the expected matrix
multiplication. So you might expect the following to produce an error, because
the dimensions are incorrect.

as.matrix(a_vec) %*% b_vec

## [,1] [,2] [,3]
## [1,] 2 2 2
## [2,] 4 4 4
## [3,] 6 6 6

At face value this is a 3 × 1 matrix, multiplied by a 3 × 1 matrix. However,
when b_vec is automatically coerced to be a matrix, R decided to make it a “row
vector”, a 1 × 3 matrix, so that the multiplication has conformable dimensions.
If we had coerced both, then R would produce an error.

as.matrix(a_vec) %*% as.matrix(b_vec)

Another way to calculate a dot product is with the crossprod() function. Given
two vectors, the crossprod() function calculates their dot product. The func-
tion has a rather misleading name.

crossprod(a_vec, b_vec) # inner product

## [,1]
## [1,] 12

tcrossprod(a_vec, b_vec) # outer product

## [,1] [,2] [,3]
## [1,] 2 2 2
## [2,] 4 4 4
## [3,] 6 6 6