# Thread: Bessel's Inequality

1. ## Bessel's Inequality

I'm trying to workout the proof for Bessel's Inequality as given in my text. I'm having trouble reconciling the version in my text with other sources. I attached screen shot of a version in my text, along with a version from another source. The one with A's and B's is from my text.

Should the inner product in the numerator be <B,Ai> ?

2. ## Re: Bessel's Inequality

yes.

$B$ is the element in Hilbert space being described.

The $A_i$'s are the orthonormal sequences