Suppose that C is an n * n symmetric idempotent matrix with
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Suppose that C is an n * n symmetric idempotent matrix with rank r and let V ? N(0n, In). a. Show that C = AA?, where A
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Suppose that C is an n * n symmetric idempotent matrix with rank r and let V ? N(0n, In). a. Show that C = AA?, where A is n * r with A?A = Ir. (Hint: C is positive semidefinite and can be written as Q?Q?, as explained in Appendix 18.1.) b. Show that A?V ? N10r, Ir2. c. Show that V?CV ? x2
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