Assignment 3 - Qn 7 Clarification

[vijay....@gmail.com]

Claim :F = \int_0^1 |f(t)|^2 dt is a norm

In the definition of a norm, the above form F does not satisfy the scaling property.

|\alpha F| \neq |\alpha| |F|. On the other hand F^{1/2} is a valid norm.

Kindly clarify

[nikunj]

yeah you are correct, F is not valid definition of norm since it does not satisfy scaling property.
F^{1/2} is a valid norm which is nothing but euclidean norm or L_2 norm for signal defined in interval [0,1].

Regards
TA