Functional Analysis Overview
Published at : 25 Dec 2020
In this video, I give an overview of functional analysis, also known as infinite-dimensional linear algebra. Functional analysis is a fascinating sub-field of math that combines both linear algebra and analysis, with a sprinkle of topology. Among others, I prove that boundedness of linear operators is equivalent to continuity, and I give an example of an unbounded operator, and I go over major theorems like the open mapping theorem or the closed graph theorem. Finally, I give a brief overview of Hilbert spaces. Enjoy!