Infinite matrices.

  • Thread starter cragar
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  • #1
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If I had an infinite matrix [itex] \aleph_0 \times \aleph_0 [/itex] could I find the eigenvalues or the Determinant of this matrix. I think some of these matrices would have a finite Determinant or it could be zero. Because i could add 1/2+1/4+1/8..... but I would just need a matrix with the right entries. Just wondering if anyone has done this and how you would go about figuring it out.
 

Answers and Replies

  • #2
chiro
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Hey cragar.

The topic that deals with this kind of thing is the Hilbert-Space theory that deals with operator algebras in infinite-dimensional spaces.

If you want to look into this look into things like Hilbert-Space Theory, Banach Spaces, and operator algebras like C* algebras as well as functional analysis in the infinite-dimensional spaces.
 
  • #3
HallsofIvy
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Note that you will need to have some kind of "regularity conditions" on the "infinite matrices" in order that the infinite sums involved will converge.
 
  • #4
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Hey cragar.

The topic that deals with this kind of thing is the Hilbert-Space theory that deals with operator algebras in infinite-dimensional spaces.

If you want to look into this look into things like Hilbert-Space Theory, Banach Spaces, and operator algebras like C* algebras as well as functional analysis in the infinite-dimensional spaces.
Can you recommend any sources related to these topics? Thanks.
 

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