[VECTOR SPACES 4] Function Vector Spaces

Function Vector Spaces, functions are vectors, intuitive understanding, measuring distances, the inner product with functions, orthogonal functions, projecting functions onto functions.

King's College London - Physics Programme -
Year 1 Maths Video Lecture

CONTENTS:
- Functions f(x) fulfill vector space axioms [0:42]
(see previous video to refresh vector space axioms https://youtu.be/lZXMNRKFqKk )
- Dimensions of a function vector space [2:33]
- Interpretation of function vectors as sampled points [3:20]
- Basis for function vector space - sampling approach, introduction to Dirac Delta [5:22]
- Other basis for function vector space - powers of x [8:26]
- Inner product for function vector space - Introduction & intuition [9:20]
- Inner product for function vector space - Definition [13:17]
- Length of a function vector - [14:02]
- Orthogonality between functions - examples [14:39]
- Other things to do with inner product between functions [15:59]
- Summary of this video and previous one: Inner product summary [16:15]

Francisco (Paco) Rodríguez Fortuño
Senior Lecturer King's College London

Видео [VECTOR SPACES 4] Function Vector Spaces канала PacoVideoLectures