Mathematics-Online lexicon: Quadratic Form

	[home] [lexicon] [problems] [tests] [courses] [auxiliaries] [notes] [staff]
	Mathematics-Online lexicon:
	Quadratic Form

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

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.

Annotation:

automatically generated 6/25/2018