MAI391_-_FA_2024_-_RE_3066.webp

Kizspy | Question: 15
(Choose 1 answer)
(See picture)
A. (i)
B. (ii)
C. (iii)
D. (iv)
Given the singular value decomposition of A:A=[\begin{matrix}\frac{\sqrt{2}}{2}&-\frac{\sqrt{2}}{2}\\ \frac{\sqrt{2}}{2}&\frac{\sqrt{2}}{2}\end{matrix}][\begin{matrix}3&0\\ 0&\sqrt{3}&0\end{matrix}][\begin{matrix}\frac{\sqrt{2}}{2}&\frac{\sqrt{2}}{2}&0\\ \frac{\sqrt{6}}{6}&-\frac{\sqrt{6}}{3}&\frac{\sqrt{6}}{3}\end{matrix}]Denote by \hat{A}(1) the 1-rank approximation of A.The spectral norm of A-\hat{A}(1) is:
(i) 1
(ii) \sqrt{2}
(iii) \sqrt{3}
(iv) \sqrt{6}