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Unformatted text preview: P x and P y commute then either L x and L y are the same or they are orthogonal. 5 Let X be an n p matrix (assume n p ) and let W be the space spanned by the columns of X . A Show that if rank( X ) = p then X X is invertible, and P = X ( X X )1 X is the orthogonal projection onto W . B Show that if rank( X ) = r < p and X is any matrix having r columns that form a basis for C ( X ) , then P = X ( X X )1 X is the orthogonal projection onto W ....
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 Spring '08
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