Is a sufficient condition for a $2\times 2$ matrix $$\left(\begin{array}{cc}a&b\\b&d\end{array}\right)$$ to be positive definite that $a >0$ and $ad > b^2$ ?
Sufficient condition for a matrix to be positive definite
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linear-algebra
matrices
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0Do you mean, a $2\times 2$ matrix $$\left(\begin{array}{cc}a&b\\d&c\end{array}\right)\ ?$$ – 2012-04-19
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0Welcome to math.SE. For future reference, soft-questions are more non-mathematical in nature. I've changed to more appropriate tags. – 2012-04-19
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0@ArturoMagidin: The $c$ and $d$ are interchanged. – 2012-04-19
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1@Robb: Arturo wrote it like you said it. If you interchange $c$ and $d$, then they're not clockwise. – 2012-04-19
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0@ArturoMagidin: Actually you are correct. – 2012-04-19
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0@Robb: Which is it? The one I wrote in the comment, or the one I put in the question? – 2012-04-19
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0@ArturoMagidin: The one you put in the question. – 2012-04-19