試題詳解

7. For a non-zero matrix A ∈ , deine
(1)
the maximum Frobenius norm ||A  x llover all unit-norm vectors  x . Which of the following
statements is/are true?
(A) σ² is the maximal eigenvalue of .
(B) If x₀ is an optimal solution to equation (1), i.e, llAx₀ll = σ, then there exists a vector
x₁ such that Ax₁ = 0  and ≠0.
(C) Assune m = n and A is nonsingular. Then = .
(D) Assume m = n. Then t A is singular only if σ ≥ 1.

(E) None of the above is true.