Unformatted text preview: y-ˆ y 1 k 2 + 2( y-ˆ y ) t (ˆ y-ˆ y 1 ) = k y-ˆ y k 2 + k ˆ y-ˆ y 1 k 2 . 2) Show that any symmetric and idempotent matrix M is a projection matrix. Sol) Suppose M has the two properties. Note that ( I-M ) M = M-M 2 = M-M = 0 . So, for any y in R k , its residual vector y-M y is orthogonal to C ( M ) because ( y-M y ) t M = y t ( I-M ) t M = y t ( I-M ) M = 0 . Therefore, M is a projection matrix....
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This note was uploaded on 04/29/2010 for the course STAT stat 426 taught by Professor Xe during the Spring '10 term at University of Illinois at Urbana–Champaign.
- Spring '10