Linear Algebra and the C Language/a0cp


Quadratic forms: M[R3,C3]

  • Geometric meaning :

If all eigenvalues of A are non-zero, then the solution set is an ellipsoid or a hyperboloid. If all the eigenvalues are positive, then it is an ellipsoid; if some eigenvalues are positive and some are negative, then it is a hyperboloid; if the eigenvalues are all equal and positive, then it is a sphere. Wikipedia: Quadratic form 

  Consider the case of quadratic forms in three variables x, y, z.
  
   a x^2  +  b y^2  +  c z^2   +  d xy  +  e xz  +  f yz = C
        
  The Associated symmetric matrix A has the form:
  
                    a     d/2    e/2
              A =  d/2     b     f/2
                   e/2    f/2     c

The application

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