crossprod {base}R Documentation

Matrix Crossproduct


Given matrices x and y as arguments, return a matrix cross-product. This is formally equivalent to (but usually slightly faster than) the call t(x) %*% y (crossprod) or x %*% t(y) (tcrossprod).


crossprod(x, y = NULL)

tcrossprod(x, y = NULL)


x, y

numeric or complex matrices (or vectors): y = NULL is taken to be the same matrix as x. Vectors are promoted to single-column or single-row matrices, depending on the context.


A double or complex matrix, with appropriate dimnames taken from x and y.


When x or y are not matrices, they are treated as column or row matrices, but their names are usually not promoted to dimnames. Hence, currently, the last example has empty dimnames.

In the same situation, these matrix products (also %*%) are more flexible in promotion of vectors to row or column matrices, such that more cases are allowed, since R 3.2.0.


Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language. Wadsworth & Brooks/Cole.

See Also

%*% and outer product %o%.


(z <- crossprod(1:4))    # = sum(1 + 2^2 + 3^2 + 4^2)
drop(z)                  # scalar
x <- 1:4; names(x) <- letters[1:4]; x
tcrossprod(as.matrix(x)) # is
tcrossprod(x)            # no dimnames

m <- matrix(1:6, 2,3) ; v <- 1:3; v2 <- 2:1
stopifnot(identical(tcrossprod(v, m), v %*% t(m)),
          identical(tcrossprod(v, m), crossprod(v, t(m))),
          identical(crossprod(m, v2), t(m) %*% v2))

[Package base version 3.3.2 Index]