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section on optimization |
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:<math>x=-A^{-1}b.</math>
If the quadratic form, and hence ''A'', is positive definite, the [[second partial derivative test|second-order condition]]s for a minimum are met at this point. If the quadratic form is negative definite, the second-order conditions for a maximum are met.
An important example of such an optimization arises in [[multiple regression]], in which a vector of estimated parameters is sought which minimizes the sum of squared deviations from a perfect fit within the dataset.
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