# Hilbert spaces

A senior thesis by Jacob Druell, Fall 2022

*Abstract*: Inner product spaces are vector spaces along with an inner product on the vector space. Inner products allow for formal definitions of angles, lengths, and orthogonality of vectors. Inner product spaces are useful for linear algebra, data science, machine learning, functional analysis, and even quantum mechanics. Before we get too far into Inner product spaces, some introductory definitions will be provided for reference. During this presentation we will focus more on concepts rather than proofs, so proofs will be absent from the poster.