試題詳解

六、 The Householder matrix H = is the orthogonal
projection matrix onto some nonzero vector , is a reflection matrix. Which of the
following statements is/are true?
(A) Consider the 2-dimensional space, ie. n = 2. For vectors u, d, p,q   shown in the
figure below, we have H d = p.
(B) H is a symmetric and orthogonal matrix.
(C) Both linear systems A z = o and HAz = Ho are equivalent.
(D) Let a = ≠0. Then llull² = -2 llαll u₁

and Hα =
(E) None of the above are true.