Abstract
We give some new canonical representations for forms over C. For example, a general binary quartic form can be written as the square of a quadratic form plus the fourth power of a linear form. A general cubic form in .x1,..xn/ can be written uniquely as a sum of the cubes of linear forms lij (xi,..xj ), 1 ≤ i ≤ j ≤ n. A general ternary quartic form is the sum of the square of a quadratic form and three fourth powers of linear forms. The methods are classical and elementary.
Original language | English (US) |
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Pages (from-to) | 185-220 |
Number of pages | 36 |
Journal | Pacific Journal of Mathematics |
Volume | 266 |
Issue number | 1 |
DOIs | |
State | Published - 2013 |
Keywords
- Canonical forms
- Sums of powers of polynomials
ASJC Scopus subject areas
- General Mathematics