- #1

gfd43tg

Gold Member

- 953

- 49

## Main Question or Discussion Point

Hello,

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?

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?