Moebius transformations

mob(M, x)
M %mob% x

Arguments

M: 2-by-2 matrix of integers
x: vector of values to be transformed

Value

Returns a value with the same attributes as x. Elementwise, if

$$M=\left(\begin{array}{cc}a&b\\c&d\end{array}\right)$$

then mob(M,x) is $\frac{ax+b}{cx+d}$.

References

Wikipedia contributors, "Mobius transformation," Wikipedia, The Free Encyclopedia (accessed February 13, 2011).

Author

Robin K. S. Hankin

Note

This function does not check for M being having integer elements, nor for the determinant being unity.

Examples

M <- matrix(c(11,6,9,5),2,2)
x <- seq(from=1+1i,to=10-2i,len=6)

M %mob% x
#> [1] 1.821656+0.0063694268i 1.825780+0.0008316008i 1.828228-0.0001879346i
#> [4] 1.829539-0.0004195951i 1.830330-0.0004653946i 1.830854-0.0004577707i
plot(mob(M,x))