here is some question of what is meant by "empty" here but this will test if matrix m has zero length:
length(m) == 0
Regarding initializing a matrix this initializes it to be a 0x0 matrix:
m <- matrix(, 0, 0)
and this initalizes it to be a 1x1 matrix containing NA:
m <- matrix()
and this initializes it to an nr by nc matrix of NA values:
m <- matrix(, nr, nc)