A linear manifold is a nonempty subset 
of a Hilbert
space 
that is closed under addition
of vectors and scalar multiplication.
Linear Manifold
See also
Hilbert Space, Subspace, Vector Space, von Neumann AlgebraPortions of this 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