試題詳解

7、For a non-zero matrix A∈R^m✕n, define the maximum Frobenius norm||Ax|| over all unit-norm vectors x. Which of the following statements is/are true?
(A)σ² is the maximal eigenvalue of AA^T.
(B) If x₀ is an optimal solution to equation (1), i.e., ||Ax₀||= σ, then there exists a vector x1 such that Ax₁ = 0 and x₁^Tx_0≠0.
(C) Assume m = n and A is nonsingular. Then.
(D) Assume m = n. Then I_n + A is singular only if σ≥ 1.
(E) None of the above is true.