crossprod {base} | R Documentation |

## Matrix Cross-Product

### Description

Given matrices `x`

and `y`

as arguments, return a matrix
cross-product. This is formally equivalent to (but faster than) the call
`t(x) %*% y`

(`crossprod`

) or
`x %*% t(y)`

(`tcrossprod`

).

These are generic functions since **R** 4.4.0: methods can be written
individually or via the `matOps`

group
generic function; it dispatches to S3 and S4 methods.

### Usage

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

### Arguments

`x` , `y` |
numeric or complex matrices (or vectors): |

`...` |
potential further arguments for methods. |

### 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.

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.

The propagation of `NaN`

/`Inf`

values, precision, and performance of matrix
products can be controlled by `options("matprod")`

.

### References

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

### See Also

### 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))
```

*base*version 4.4.0 Index]