Question: Exercise 10.13 Show that Cov(BY ) = 0 iff B = B Q for some matrix B. Hint: First, decompose B into the sum

Exercise 10.13 Show that Cov(BY ) = 0 iff B = B

∗ Q for some matrix B∗.

Hint: First, decompose B into the sum of two matrices B0 and B1 with C(B0) ⊂

C(V) and C(B1) ⊥ C(V). Then use a singular value decomposition of V to show that B

0V B0 = 0 iff B0 = 0.

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