Uniform superposition

For a natural number $N$ (the sole, explicit argument), uniformSuperposition N is defined as the vector in $\mathbb{C}^N$ (with the standard inner product $\langle x,y\rangle=\sum_{i=0}^{N-1}\overline{x_i}\,y_i$) all of whose $N$ coordinates take the same value, namely the complex number obtained by casting the real number $1/\sqrt{N}$ into $\mathbb{C}$ (i.e. the value $\tfrac{1}{\sqrt N}+0i$ in every coordinate $i=0,\dots,N-1$). Here $\sqrt{N}$ and the reciprocal are the total (junk-valued) real-number operations of the ambient library: at $N=0$, $\sqrt{0}=0$ by convention and $1/0=0$ by convention, so the formula that would fill each coordinate evaluates to $0$ in that degenerate case — though for $N=0$ the space $\mathbb{C}^N$ has no coordinates at all, so the vector is vacuously the unique element of $\mathbb{C}^0$ regardless of this value. No hypothesis that $N>0$ (or that $N$ is a perfect square, etc.) is imposed anywhere.