Orthogonal bases

In this lecture we continue our study of orthogonality in inner product spaces. The aim of the lecture is to extend the notion of orthonormal bases to the general Hilbert spaces.

0:00 Introduction
0:39 Motivational example
4:53 Plan of the lecture
8:15 Gram-Schmidt orthogonalisation
22:20 Bessel's inequality
27:10 Series in Hilbert spaces
37:47 Orthogonal bases
39:25 Criterion for a sequence to be an orthonormal basis