Mathematics-Online lexicon: Quadratic Form

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	Mathematics-Online lexicon:
	Quadratic Form

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For a (real) symmetric matrix

the expression

$\displaystyle a(x) =x^{\operatorname t}A x$

is called quadratic form.

Dependent on the sign of the eigenvalues of we distinguish between three types:

elliptic: All eigenvalues have the same sign.
parabolic: At least one eigenvalue equals zero and the other eigenvalues have the same sign.
hyperbolic: There are two eigenvalues of different sign.

Example:

automatically generated 6/25/2018