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Why applying the covariance matrix to the original vector will turn the vector to the direction of largest variance? How do I intuitively understand this?

And what does the inverse of the covariance matrix do? What happens when applying the inverse of covariance matrix to a vector repeatedly?

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    I'm voting to close this question as off-topic because it's been asked and answered on [Cross Validated](http://stats.stackexchange.com/): [Covariance matrix as linear transformation](http://stats.stackexchange.com/q/259058). – 2017-02-09

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