A linear manifold is a subset 
of a Hilbert space 
if it is closed under addition
of vectors and scalar multiplication.
Linear Manifold
See also
Hilbert Space, Subspace, Vector Space, von Neumann AlgebraThis entry contributed by Christopher Stover
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References
Loss, M. "A Synopsis of Hilbert Space Theory." 2014. https://loss.math.gatech.edu/14SPRINGTEA/h-space.pdf.Referenced on Wolfram|Alpha
Linear ManifoldCite this as:
Weisstein, Eric W., with contributions by Christopher Stover. "Linear Manifold." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/LinearManifold.html