Exercise Solution 3.18

We first solve for k. By our multidimensional identity [3.31]:

[s1]

so we seek a factorization Σ_X = 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]