I don't think there is anything in this article that actually demands bra-ket notation (a state in some Hilbert space), that couldn't be more clearly written wi

I don't think there is anything in this article that actually demands bra-ket notation (a state in some Hilbert space), that couldn't be more clearly written with standard notation for a Euclidean inner/outer product, but I suppose everyone has their own preferences for notation.