题目

15.(5.0分)下列说法错误的是().A. 矩阵A的谱半径与算子范数满足 rho (A) le mid mid A mid midB. 设φ为正交矩阵,则| QA |_(F)= mid AQ mid _(F)= mid A mid mid _(F)C. 实对称矩阵A的特征值为 lambda _(1), lambda _(2), ... , lambda _(n), _则 A mid _(F)= lambda _(1)^2+ lambda _(2)^2+ ... + lambda _(n)^2D. A为非奇异矩阵, B=A^TA, _则 Cord_(2)(B)=(Cond_(2)(A))^{2

15.(5.0分)下列说法错误的是().

A. 矩阵A的谱半径与算子范数满足 \rho (A) \le \mid \mid A \mid \mid

B. 设φ为正交矩阵,则| QA \ |_{F}= \mid AQ \mid _{F}= \mid A \mid \mid _{F}

C. 实对称矩阵A的特征值为 \lambda _{1}, \lambda _{2}, \cdots , \lambda _{n}, _则 A \mid _{F}= \lambda _{1}^{2}+ \lambda _{2}^{2}+ \cdots + \lambda _{n}^{2}

D. A为非奇异矩阵, B=A^{T}A, _则 Cord_{2}(B)=(Cond_{2}(A))^{2

题目解答

C. 实对称矩阵A的特征值为 \lambda _{1}, \lambda _{2}, \cdots , \lambda _{n}, _则 A \mid _{F}= \lambda _{1}^{2}+ \lambda _{2}^{2}+ \cdots + \lambda _{n}^{2}