where on the right denotes the complex
modulus. The -norm
is the vector norm that is commonly encountered in
vector algebra and vector operations (such as the dot
product), where it is commonly denoted . However, if desired, a more explicit (but more cumbersome)
notation can be used to emphasize the distinction
between the vector norm and complex modulus together with the fact that the -norm is just one of several possible
types of norms.

For real vectors, the absolute value sign indicating that a complex modulus is being taken on the right of equation (2)
may be dropped. So, for example, the -norm of the vector is given by

(3)

The -norm is also known as the Euclidean
norm. However, this terminology is not recommended since it may cause confusion with
the Frobenius norm (a matrix
norm) is also sometimes called the Euclidean norm. The -norm of a vector is implemented in the Wolfram
Language as Norm[m,
2], or more simply as Norm[m].

The "-norm"
(denoted with an uppercase )
is reserved for application with a function ,

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.