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I've been reading two (peer reviewed) papers that use Principal Component Analysis to solve a problem I'm interested in, they both state they find the eigenvalues for the correlation matrix using the equation

$$ | \lambda I - A| = 0. $$

When I've read around PCA and eigenvalue decomposition, the appropriate equation seems to be defined as

$$ | A - \lambda I | = 0. $$

Could anyone explain to me why there might be a difference, and what the impact of this may be?

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    $\begingroup$ An equation $f(x) =0$ has the same roots as $-f(x)=0$. $\endgroup$ – amoeba Jul 20 '15 at 10:49
  • $\begingroup$ Addition/subtraction of matrices is commutative (independent of the order of the matrices, of course with adapting of the sign in case of subtraction). After that, if the determinant $\det(C)=0$ then is also $ \det(-C)=-0=0$ $\endgroup$ – Gottfried Helms Jul 20 '15 at 10:56
  • $\begingroup$ Much appreciated, thanks. It's been a while since I've had to do anything outside of adding and subtracting! $\endgroup$ – DarkRyuu Jul 20 '15 at 11:13
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    $\begingroup$ @Gottfried $\det(-C) = \det(C)$ when the dimensions of $C$ are even--but your argument still holds. $\endgroup$ – whuber Jul 20 '15 at 12:03

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