Homepage › Solution manuals › Gilbert Strang › Linear Algebra and Learning from Data › Exercise 4.2.4
We have (CD)qk = CDqk = Cλk(D)qk = λk(D)Cqk = λk(D)λk(C)qk, on the other hand (CD)qk = λk(CD)qk, so we have λk(CD) = λk(D)λk(C)