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Linear Algebra and the C Language/a0cr
Reference material by Wikibooks contributors. This retains its source identity and is not 411 news reporting.
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Quadratic forms: M[R2,C2]
Geometric meaning :
The product of the eigenvalues is greater than zero give an ellipse or a circle.
The product of the eigenvalues is less than zero give an hyperbola.
Consider the case of quadratic forms in two variables x, y.
a x^2 + b y^2 + c xy = C
The Associated symmetric matrix A has the form:
a c/2
A =
c/2 b
The application
Ellipse. Circle ...... Wikipedia: Ellipse
Hyperbola ............ Wikipedia: Hyperbola