Exercise Solution 3.18
We first solve for k. By our multidimensional identity [3.31]:
[s1]
so we seek a factorization ΣX = kk′. Applying a Cholesky factorization, we obtain:
[s2]
Solving next for d, by our multidimensional identity [3.30]:
[s3]
[s4]
[s5]
[s6]
Accordingly, our transformation is:
[s7]