I have the following vector $Y^{T} = [Y_{1,1},Y_{1,2},\dots,Y_{N,M}]$ and $\alpha > 0$. Is it possible to write the following expression in terms of $Y$
$$ S = \sum_{i=1}^{N}{\left(\sum_{j=1}^{M}{Y_{i,j}^2}\right)^{\frac{1}{\alpha}}} $$
For $\alpha = 1$, I can say $S = Y^{T}Y$. However, for the general case, I fail to see how to do this.