Linear dependence of powers of linear forms
Abstract
The main goal of the paper is to examine the dimension of the vector space spanned by powers of linear forms. We also find a lower bound for the number of summands in the presentation of zero form as a sum of d-th powers of linear forms.
Keywords
linear form; sums of powers of linear forms; ticket of the set of polynomials
References
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3. Reznick B., Sums of even powers of real linear forms, Memoirs Amer. Math. Soc. 96 (1992), no. 463.
4. Reznick B., Patterns of dependence among powers of polynomials, DIMACS Ser. Discrete Math. Theoret. Comput. Sci. 60 (2003), 101–121.
Instytut Matematyki, Uniwersytet Śląski w Katowicach Poland
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