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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