Linear Algebra and the C Language/a0cr


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

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