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# Polynomial Norm

For a polynomial

 (1)

several classes of norms are commonly defined. The -norm is defined as

 (2)

for , giving the special cases

 (3) (4) (5)

Here, is called the polynomial height. Note that some authors (especially in the area of Diophantine analysis) use as a shorthand for and as a shorthand for , while others (especially in the area of computational complexity) used to denote the -norm and (Zippel 1993, p. 174).

Another class of norms is the -norms, defined by

 (6)

for , giving the special cases

 (7) (8) (9)

(Borwein and Erdélyi 1995, p. 6).

Bombieri Norm, Matrix Norm, Norm, Unit Circle, Vector Norm

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## References

Borwein, P. and Erdélyi, T. "Norms on ." §1.1.E.3 in Polynomials and Polynomial Inequalities. New York: Springer-Verlag, pp. 6-7, 1995.Zippel, R. Effective Polynomial Computation. Boston, MA: Kluwer, 1993.

Polynomial Norm

## Cite this as:

Weisstein, Eric W. "Polynomial Norm." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PolynomialNorm.html