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From linear algebra i understood that if the system of linear equations are independent of each other and if the number of equations is more than the number of variable, then the system is inconsistent (no solution).

Can one extend this to a system of homogeneous polynomial equations and say that:

If the polynomial equations are independent, and if the number of equations are more than the number of variables, then the system is inconsistent.

Can you tell me some reference books where i can look for such statement on polynomial equations.

Thanks in advance.

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1 Answer 1

No, you cannot extend this easily. The question of what the solution space of a finite set of (homogenous) polynomials looks like is one of the starting points of Algebraic Geometry, and there are various examples that show that this kind of question is fairly non-trivial.

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Thank you very much. –  karthik May 15 '12 at 17:06

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