Question: Problem 10 . Let V be a finite dimension inner product space and WV a subspace of V . We know that I W I

Problem 10 . Let V be a finite dimension inner product space and WV a subspace of V . We know that I W I W ie . if WE hen there exist unique we W and whew ! satisfying = w + w ( a ) Let I : V V be the linear operator satisfying o - wit u it . Prove that I is both hermitian and an isometry . ( See Problem 6 for the definition of an isometry . ) ( 6 ) Let I : V V be a linear operator that is both hermitian and an isometry . Show that there exists a subspace WV of V such that I ( 0 ) w - wt where a w t it with we W and we WI

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