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L^1-Norm

A vector norm defined for a vector

x=[x_1; x_2; |; x_n],

with complex entries by

|x|_1=sum_(r=1)^n|x_r|.

The L^1-norm |x|_1 of a vector x is implemented in the Wolfram Language as Norm[x, 1].

See also

L1-Space, L2-Norm, L-infty-Norm, Vector Norm

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References

Gradshteyn, I. S. and Ryzhik, I. M. Tables of Integrals, Series, and Products, 6th ed. San Diego, CA: Academic Press, pp. 1114-1125, 2000.Horn, R. A. and Johnson, C. R. "Norms for Vectors and Matrices." Ch. 5 in Matrix Analysis. Cambridge, England: Cambridge University Press, 1990.

Cite this as:

Weisstein, Eric W. "L^1-Norm." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/L1-Norm.html

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