Recent content by waddles

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    Span of a linearly independent subset of a hilbert space is a subspace iff finite

    Homework Statement Let S be a linearly independent subset of a Hilbert space. Prove that span(S) is a subspace, that is a linear manifold and a closed set, if and only if S is finite. Homework Equations The Attempt at a Solution Assuming S is finite means that S is a closed set...
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    Length of a curve on a sphere using calc of variations

    I have an assignment question here using calculus of variations. Question: Show that the length ℓ of a curve on the surface of a sphere of radius a is ℓ=int sqrt(theta_dot^2+(sin(theta))^2*phi_dot^2) dt Hence show that the shortest distance between two points on the sphere is given by part...