Page 40 - Applied Statistics with R

40 CHAPTER 3. DATA AND PROGRAMMING

These functions could be very useful later. When used with matrices and
as arguments, it calculates

⊤
.
When dealing with linear models, the calculation

⊤

is used repeatedly.

C_mat = matrix(c(1, 2, 3, 4, 5, 6), 2, 3)
D_mat = matrix(c(2, 2, 2, 2, 2, 2), 2, 3)

This is useful both as a shortcut for a frequent calculation and as a more efficient
implementation than using t() and %*%.

crossprod(C_mat, D_mat)

## [,1] [,2] [,3]
## [1,] 6 6 6
## [2,] 14 14 14
## [3,] 22 22 22

t(C_mat) %*% D_mat

## [,1] [,2] [,3]
## [1,] 6 6 6
## [2,] 14 14 14
## [3,] 22 22 22

all.equal(crossprod(C_mat, D_mat), t(C_mat) %*% D_mat)

## [1] TRUE

crossprod(C_mat, C_mat)

## [,1] [,2] [,3]
## [1,] 5 11 17
## [2,] 11 25 39
## [3,] 17 39 61