Talk:Schur complement

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Should it be mentioned that Schur's complement is produced by Gauss-reducing the matrix M for all the pivots in D? That's what it is about isn't it, what linear regression does to the variance matrix - Martin Vermeer

[edit] "conditional variance" in the applications section

There, it is claimed that:

the conditional variance of X given Y is the Schur complement of C in V:

\operatorname{var}(X\mid Y)=A-BC^{-1}B^T.

To me, \operatorname{var}(X\mid Y) is a function of the random variable Y; hence a random variable itself. I don't' see any Y-dependence above, so to me, the implication is that this function is constant for all values of Y; is this a consequence of the normality assumption? Btyner 22:18, 10 February 2006 (UTC)

It's a consequence of joint normality. See multivariate normal distribution. Of course one can easily construct other -- non-normal examples in which the conditional variance does not depend on Y, but differs from the unconditional variance. But in a more general setting, the conditional variance given Y would depend on Y. Michael Hardy 01:19, 11 February 2006 (UTC)
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