Vector Norm

Author

Eric W. Weisstein
March 7, 2002

This notebook downloaded from http://mathworld.wolfram.com/notebooks/LinearAlgebra/VectorNorm.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/VectorNorm.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Initialization

<<LinearAlgebra`MatrixManipulation`

?VectorNorm

Definition

((((∑_i)\[VerticalSeparator](Subscript[v, i])(\[VerticalSeparator]^p)))^(1/p))

v={1,2,3}

Table[{p,VectorNorm[v//N,p]},{p,5}]

Table[{p,VectorNorm[v,p]},{p,5}]

VectorNorm[v_List?VectorQ,p_Integer?Positive]:=(Plus@@(Abs[v]^p))^(1/p)

FullSimplify[Table[{p,VectorNorm[v,p]},{p,5}]]

N[%]