R: Matrix Crossproduct

crossprod {base} | R Documentation

## 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`.

### Note

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.

### 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))

[Package base version 3.1.2 Index]