1.2 Vector Spaces - #11 Function Vector Spaces (Special) (Optional)

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    • 1.2 Vector Spaces - #06 N-Dimensional...   )
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