Suppose Q(x) = x" Ax %D for some symmetric matrix А, and that we have a diagonal matrix D and a non-orthogonal matrix P such that D = P¯'AP. Then the smallest diagonal entry of D is the minimum value of Q(x) on ||x|| = 1. %3D True False

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Suppose
Q(x) = x"Ax
for some symmetric matrix
А,
and that we have a diagonal matrix
D
and a non-orthogonal matrix
P
such that
D = P¯'AP.
Then the smallest diagonal entry of
D
is the minimum value of
Q(x)
on
||x|| = 1.
%3D
True
False
Transcribed Image Text:Suppose Q(x) = x"Ax for some symmetric matrix А, and that we have a diagonal matrix D and a non-orthogonal matrix P such that D = P¯'AP. Then the smallest diagonal entry of D is the minimum value of Q(x) on ||x|| = 1. %3D True False
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