Second-degree homogeneous expressions are called quadratic forms. They occur in physics and in geometry. In analytical geometry, for instance, a quadratic form has to be transformed into its principal-axes-form so as to determine the nature of the conicsection such as parabola, ellipse or hyperbola, *etc.*, if it involves two variables, and of the quadratic surface such as paraboloid, ellipsoid or hyperboloid, *etc.*, if it involves three variables. A quadratic form can be represented by

where *X* is a column *n*-vector and *A* is a symmetric matrix of the coefficients. We study here the method of transformation of ...

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