Polarization of An Algebraic Form - Examples

Examples

  • Suppose that x=(x,y) and f(x) is the quadratic form

Then the polarization of f is a function in x(1) = (x(1), y(1)) and x(2) = (x(2), y(2)) given by

  • More generally, if f is any quadratic form, then the polarization of f agrees with the conclusion of the polarization identity.
  • A cubic example. Let f(x,y)=x3 + 2xy2. Then the polarization of f is given by

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