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ironman
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Finding How to find the conditional distribution of gaussian from covariance matrix?

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ironman
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Finding the conditional distribution of gaussian from covariance matrix

I know that the conditional distribution of two gaussian is gaussian. But in the following statement how does the Θ captures the conditional distributions?

And what do they mean by the term "captures" here?

Let's suppose X is a random variable such that X = ( X1 , X2 , . . . , Xp ) has a multivariate Gaussian distribution with mean-vector 0 (for convenience ) and covariance Σ , then Θ =Σ−1 captures the conditional distributions of each Xj given the rest.