Matrix Cross Product

crossprod

Description

Returns a matrix that is the cross product of two given matrices.

Usage

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

Arguments

x	matrix or vector, numeric or complex. Missing values (NA) are allowed.
y	matrix or vector, numeric or complex. Must have the same number of rows as x. If not specified or NULL (the default), x is used. Also, for tcrossprod, y must have the same number of columns as x. Missing values (NA) are allowed.

Details

It is better to use crossprod(x) than x %*% t(x) because crossprod(x) is faster, and, on some machines, is more accurate.

Any computation involving NA results in NA.

Vectors are taken to be columns, so crossprod(vec1,vec2) is a one-by-one matrix, with the element being the dot product of the two vectors.

tcrossprod(vec1,vec2) is the outer product of the two vectors.

Value

crossprod	returns a matrix representing the cross product of x and y, defined as t(x) %% y, where %% is matrix multiplication and t is transposition. Thus the [i,j]th element of the result is sum(x[,i]*y[,j]).
tcrossprod	returns a matrix representing the cross product of t(x) and t(y), defined as x %% t(y), where %% is matrix multiplication and t is transposition. Thus the [i,j]th element of the result is sum(x[i,]*y[j,]).

See Also

matrix, Matrix-product, outer.

Examples

amat <- matrix(c(19,8,11,2,18,17,15,19,10), nrow = 3)
crossprod(amat) # if amat has dimensions of n(rows) and p(cols)
                # the resultant matrix will be p by p
bmat <- c(9, 5, 14)
crossprod(amat, bmat)
tcrossprod(1:3, 11:13) # same as outer(1:3, 11:13)

Package base version 6.1.4-13
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