A subset 
of a Hilbert space 
is a linear manifold 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. http://people.math.gatech.edu/~loss/14SPRINGTEA/h-space.pdf.Cite this as:
Stover, Christopher. "Linear Manifold." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/LinearManifold.html