base (version 3.0.3)

crossprod: Matrix Crossproduct

Description

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).

Usage

crossprod(x, y = NULL)
tcrossprod(x, y = NULL)

Arguments

x, y

numeric or complex matrices: 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.

Value

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

References

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

See Also

%*% and outer product %o%.

Examples

(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
identical(tcrossprod(as.matrix(x)),
          crossprod(t(x)))
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))