It seems like all projections of a vector $v \in V$ to a 1-dimensional subspace represents a method of mapping $v$ to the base field $\mathbb{F}$. Is it necessarily isomorphic? And would any structures need to be defined on $V$ (e.g. metric, inner product) in order to identify this isomorphism?
2026-03-25 17:52:08.1774461128
Is the dual space of a vector space V isomorphic to the space of all linear projections of V onto a 1 dimensional subspace?
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