Resumen de On the rank of powers of a non-degenerate quadratic form
A decomposition of a homogeneous polynomial is a representation of that polynomial as a sum of powers of linear forms; in particular, the minimum number of addends in this sum is said to be the rank of the polynomial. We analyze a way to determine explicit decompositions of a polynomial corresponding to a power of a non-degenerate quadratic form. The main instrument used in this context is the Apolarity Lemma, which is a classic result relating the summands of a decomposition to its apolar ideal.
