How can I determine if two eigenvectors form an open or closed subspace?

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Sergio Manzetti 2017-12-21

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评论： Sergio Manzetti 2017-12-22

Hi, I have two eigenvectors, which form a subspace in H. Is there an easy way to determine whether the subspace they form is open or closed in H?

Thanks

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Torsten 2017-12-21

What is H ?

Best wishes

Torsten.

Sergio Manzetti 2017-12-21

编辑：Sergio Manzetti 2017-12-21

Hi Torsten, H=Hilbert space (L^2[-inf, +inf]).

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Torsten 2017-12-21

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http://www.math.colostate.edu/~pauld/M645/BasicHS.pdf

Best wishes

Torsten.

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Matt J 2017-12-21

编辑：Matt J 2017-12-21

From the document in Torsten's link,

"Every finite dimensional subspace of a Hilbert space H is closed."

The span of any two vectors is clearly an example of a finite dimensional sub-space and is therefore closed in L2.

Sergio Manzetti 2017-12-22

Thanks Matt. I take this is because they start from some point and are thus not infinite?

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