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## Main Question or Discussion Point

Hey guys,

I've been trying to brush up on my linear algebra and ran into this bit of confusion.

I just went through a proof that an operator with distinct eigenvalues forms a basis of linearly independent eigenvectors.

But the proof relied on a one to one mapping of eigenvalues to eigenvectors. Is there any particular reason why for a distinct eigenvalue, there shouldn't be more than one (normalized) eigenvectors that satisfies the eigenvalue definition.

And if so, how do I prove it? I'm not mentally convinced, even if that is the case as the proofs seem to indicate!

Thanks!

I've been trying to brush up on my linear algebra and ran into this bit of confusion.

I just went through a proof that an operator with distinct eigenvalues forms a basis of linearly independent eigenvectors.

But the proof relied on a one to one mapping of eigenvalues to eigenvectors. Is there any particular reason why for a distinct eigenvalue, there shouldn't be more than one (normalized) eigenvectors that satisfies the eigenvalue definition.

And if so, how do I prove it? I'm not mentally convinced, even if that is the case as the proofs seem to indicate!

Thanks!