試題詳解

15. For any given 0 ≠ w ∈ , let's consider the matrix = I − parameterized by a real scalar α. Which of the following statements are true?
(A) = , i.e. is an idempotent matrix, if and only if α ∈ {0, 1, 2}.
(B) = x for any x ∈ if and only if α ∈ {0, 1, 2}.
(C) is singular if and only if α = 1.
(D) For any x ∈, , the orthogonal complement of w, if and only if α = 1.
(E) For any x ∈ , = ‖H₁x‖₂, i.e. x has the smallest 2- norm if and only if α = 1.