Scaling Different Axes

Suppose that you wanted to transform a two-dimensional vector so that the first element doubled in size, while the second element was cut by a third.

You can do this with matrix multiplication, as the matrix A, which yields the R output:

     [,1]      [,2]
[1,]    2 0.0000000
[2,]    0 0.6666667

achieves the desired result.