# What does $\|u\|^2_2$ mean?

Given a vector $$u = (x, y, z)$$ what is $$\|u\|_2^2$$ ?

The $$\| \cdot \|_2$$ function is the $$2$$-norm, i.e. the standard Euclidean length of a vector. Thus, $$\|(x, y, z)\|_2^2 = x^2 + y^2 + z^2.$$