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Rampant_mouse
  • Member for 10 years, 11 months
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Are there any known criteria for quadratic mapping from R^n to R^n being surjective?
y1 = 2 * x1 * x3; y2 = 2 * x2 * x3; y3 = x3^2 - x1^2 - x2^2. To see it is enough to write it in polar coordinates. For higher dimensions the situation is same yj = 2 * xj * xn; yn = xn^2 - squares of other variables
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Are there any known criteria for quadratic mapping from R^n to R^n being surjective?
It is easy to see that the surjective quadratic mappings exist in every dimension. For example in dimension 3 it is the following mapping:
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Are there any known criteria for quadratic mapping from R^n to R^n being surjective?
The problem is linked to representation theory via invariant theory.
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