MATH307 April 2013
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Question 01 (d)
Find the norm and condition number of
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What special kind of matrix is ? What is the norm of this kind of matrix? How can this help you?
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Observe that = and all entries are real, so U is an orthogonal matrix. This means that
because the norm of a diagonal matrix is the entry with the largest magnitude.
and therefore, .
Next, notice that
Once again, since U is orthogonal,
we have that . Thus
therefore, cond(A) = 2
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MER QGQ flag, MER QGS flag, MER RH flag, MER RT flag, MER Tag Condition number, MER Tag Matrix norm, Pages using DynamicPageList parser function, Pages using DynamicPageList parser tag