Introduction to Econometrics 3rd Edition by James Stock, James Stock

تمرين 17

Let C be a symmetric idempotent matrix.
a. Show that the eigenvalues of C are either 0 or 1. ( Hint: Note that Cq = q implies 0 = Cq q = CCq q = CCq q = 2 q q and solve for .)
b. Show that trace( C ) = rank( C ).
c. Let d be a n × 1 vector. Show that d'Cd 0.