試題詳解

10、Let P ∈ Rⁿˣⁿ be the orthogonal projection matrix, with respect to the Euclidean inner product, of vectors in Rⁿ onto col( A ) for some nonzero matrix A ∈ Rⁿˣᵏ. Which of the following statements is/are true?
(A) tr(PᵀP) ≥ rank(P).
(B) P can have an eigenvalue larger than 2.
(C) P²x ≠x for all x ∈ Rⁿ.
(D) If k ＜ n and b ∈ Rⁿ, the system of linear equations Ax = b has a unique least squares solution.

(E) None of the above is true.