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)