Question: 19.10 Let C be a symmetric idempotent matrix. a. Show that the eigenvalues of C are either 0 or 1. (Hint: Note that Cq =

19.10 Let C be a symmetric idempotent matrix.

a. Show that the eigenvalues of C are either 0 or 1. (Hint: Note that Cq = gq implies 0 = Cq - gq = CCq - gq = gCq - gq = g2q - gq, and solve for G.)

b. Show that trace(C) = rank(C).

c. Let d be an n * 1 vector. Show that dCd Ú 0.

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