試題詳解

8. Let V together with the inner product (‧,‧)y be an inner product space over . For a
collection of N linearly independent vectors [w₁ ,...,] in V, let M = be
the corresponding Gram matrix, i.e, the (i, j)-th entry of M is given by
Define the following set of real-valued functions f : V →

which is a vector space over when combined with standard addition and scalar multiplica-
M= 1.8m (2m,3)v tion of real-valued functions. For any f( x )  =
in the vector space F, define

Which of the following statements is/are true?
(A) M is positive definite.
(B) If m_1,1 = 2, m_2,2 = 1, and m_1,2 = -, then is the vector norm induced by the inner product .
(C) (f,g)s is an inner product for elements f,g ∈ F.
(D) Given g(y) = , we have = f(ω₁) for all f ∈ F.

(E) None of the above is true.
＜f(z) =