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Let f(x)=x^(T)Ax+2b^(T)x+c , where AinR^(ntimes n) is symmetric, binR^(n) , and cinR . Suppose that A>-=0 . Show that f is bounded below ^(1) over
Let
f(x)=x^(T)Ax+2b^(T)x+c
, where
AinR^(n\\\\times n)
is symmetric,
binR^(n)
, and
cinR
.\ Suppose that
A>-=0
. Show that
f
is bounded below
^(1)
over
R^(n)
if and only if
bin
\
Range(A)={():}
Ay
{::yinR^(n)}
.
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