This is a subject I struggled with the first time I took it. Ironically, this was the engineering version of it. It wasn't until I took the rigorous, axiomatic version that everything clicked.

Functional analysis provides the theoretical foundation for understanding spaces of functions and the linear mappings between them. Central to this discipline are Banach spaces: complete normed vector ...

Normed linear spaces provide the foundational setting for modern functional analysis by equipping vector spaces with a notion of length. Within these spaces, orthogonality extends the Euclidean ...