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onako
#1
Mar6-12, 08:15 AM
P: 87
Given a symmetric matrix
[tex]A=\left(\begin{array}{ccccc}
\sum a_{1s} & & & & \\
& \ddots & & a_{ij} \\
& & \ddots & & \\
&a_{ij} & & \ddots & \\
& & & & \sum w_{as}
\end{array}\right) \in\mathbb{R}^{n\times n},
[/tex]
with strictly positive entries a_{ij}, and with the diagonal entries being sum of off-diagonal entries residing
in the corresponding row/column, how to proceed with the proof for A being positive definite,
[tex]
x^TAx>0
[/tex]
for some non-zero vector x.
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