matrix.addition {psych} | R Documentation |
It is sometimes convenient to add two vectors or matrices in an operation analogous to matrix multiplication. For matrices nXm and mYp, the matrix sum of the i,jth element of nSp = sum(over m) of iXm + mYj.
x %+% y
x |
a n by m matrix (or vector if m= 1) |
y |
a m by p matrix (or vector if m = 1) |
Used in such problems as Thurstonian scaling. Although not technically matrix addition, as pointed out by Krus, there are many applications where the sum or difference of two vectors or matrices is a useful operation. An alternative operation for vectors is outer(x ,y , FUN="+") but this does not work for matrices.
a n by p matix of sums
William Revelle
Krus, D. J. (2001) Matrix addition. Journal of Visual Statistics, 1, (February, 2001).
x <- seq(1,4)
z <- x %+% -t(x)
x
z
#compare with outer(x,-x,FUN="+")
x <- matrix(seq(1,6),ncol=2)
y <- matrix(seq(1,10),nrow=2)
z <- x %+% y
x
y
z
#but compare this with outer(x ,y,FUN="+")