Mathematik-Online lexicon: Example: Quadratic Form

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	Mathematik-Online lexicon:
	Example: Quadratic Form

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The symmetric matrix

$\begin{displaymath} A=\left( \begin{array}{cc} 1+\lambda&1-\lambda\\ 1-\lambda&1+\lambda \end{array}\right) \end{displaymath}$

has the eigenvalues

and $2\lambda$ .

Hence, the quadratic form

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

is elliptic for $\lambda > 0$ , parabolic for $\lambda=0$ and hyperbolic for $\lambda <0$ .

see also:

automatisch erstellt am 25. 6. 2018