Matrix Multiplication

Description

Multiplies two matrices, if they are conformable. If one argument is a vector, it will be promoted to either a row or column matrix to make the two arguments conformable. If both are vectors of the same length, it will return the inner product (as a matrix).

Usage

x %*% y

Arguments

Details

When a vector is promoted to a matrix, its names are not promoted to row or column names, unlike as.matrix.

Promotion of a vector to a 1-row or 1-column matrix happens when one of the two choices allows x and y to get conformable dimensions.

This operator is a generic function: methods can be written for it individually or via the matOps group generic function; it dispatches to S3 and S4 methods. Methods need to be written for a function that takes two arguments named x and y.

Value

A double or complex matrix product. Use drop to remove dimensions which have only one level.

Note

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

For matrix cross products, crossprod() and tcrossprod() are typically preferable. matrix, Arithmetic, diag.

Examples

x <- 1:4
(z <- x %*% x)    # scalar ("inner") product (1 x 1 matrix)
drop(z)             # as scalar

y <- diag(x)
z <- matrix(1:12, ncol = 3, nrow = 4)
y %*% z
y %*% x
x %*% z