# Science:Math Exam Resources/Courses/MATH307/December 2012/Question 06 (e)

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MATH307 December 2012

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### Question 06 (e)

Suppose that A is a matrix with singular value decomposition ${\displaystyle A=U\Sigma V^{*}}$ where

{\displaystyle {\begin{aligned}U=&{\begin{bmatrix}1/{\sqrt {2}}&1/{\sqrt {2}}&0\\1/{\sqrt {2}}&-1/{\sqrt {2}}&0\\0&0&1\end{bmatrix}}\\\Sigma =&{\begin{bmatrix}2&0&0\\0&1&0\\0&0&1/2\end{bmatrix}}\\V=&{\begin{bmatrix}1/{\sqrt {3}}&0&2/{\sqrt {6}}\\1/{\sqrt {3}}&1/{\sqrt {2}}&-1/{\sqrt {6}}\\1/{\sqrt {3}}&-1/{\sqrt {2}}&-1/{\sqrt {6}}\end{bmatrix}}\end{aligned}}}

(e) What are the matrix norm ${\displaystyle \|A^{-1}\|}$ and the condition number of A?

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MER QGQ flag, MER RH flag, MER RS flag, MER RT flag, MER Tag Condition number, MER Tag Matrix decomposition, Pages using DynamicPageList parser function, Pages using DynamicPageList parser tag
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