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== Quadratic forms ==
{{Main|Definite quadratic form}}
The (purely) [[quadratic form]] associated with a real <math>\ n \times n\ </math> matrix <math>\ M\ </math> is the function <math>\ Q : \mathbb{R}^n \to \mathbb{R}\ </math> such that <math>\ Q(\mathbf{x}) = \mathbf{x}^\top M \mathbf{x}\ </math> for all <math>\ \mathbf{x} ~.</math> <math>\ M\ </math> can be assumed symmetric by replacing it with <math>\ \tfrac{1}{2} \left(M + M^\top \right)\ ,</math> since any
A symmetric matrix <math>\ M\ </math> is positive definite if and only if its quadratic form is a [[strictly convex function]].
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