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I am having a question regarding how eigenfunctions are orthogonal in Hilbert space, or what does that even mean (other than the inner product is zero). I mean, I know in ##\mathbb {R^{3}}##, vectors are orthogonal when they are right angles to each other.

However, how can functions be "orthogonal", in the sense of being perpendicular, and does Hilbert Space have infinite dimensions?

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# Eigenfunctions orthogonal in Hilbert space

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