Linear Algebra and the C Language/a0cp

__NOTOC__ 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 Ellipsoid ............................... Wikipedia: Ellipsoid Hyperboloid of one sheet .... Wikipedia: Hyperboloid Hyperboloid of two sheets ... Wikipedia: Hyperboloid