Functions are Vectors? Fourier Series and an Illustration of the Why #SoME2

This is my submission to 3blue1brown's Summer of Math Exposition 2. Link to Khan Academy Video on Dot Product Linearity and Symmetry: https://www.khanacademy.org/math/line... Link to 3blue1brown Video on Equivalence of Dot Product Formulations:    • Dot products and duality | Chapter 9, Esse...   Link to Linda Green Video on Equivalence of Dot Product Formulations:    • The Two Definitions of Dot Product Are Equ...   Link to Rafay Anwar Video on Orthogonality Proofs:    • Proof of Orthogonality of Trigonometric Fu...   Link to 3blue1brown Video on Cramer's Rule:    • Cramer's rule, explained geometrically | C...