Orthogonality of eigenfunctions
Channel: MatheMagician
Date: 2023-11-11

When we want to find the Fourier series of a function f(x), we are basically writing f(x) as a linear combination of functions phi_n(x)  and psi_n(x), where phi_n(x)= sin(n pi x/L) and psi_n(x)= cos(n pi x/L). In linear algebra terms: the phi_n and psi_n are our basis vectors and the coefficients a_n and b_n are our coordinates with respect to this basis. What really helps us here that the phi_n and psi_n are not just any basis, but in fact an orthogonal basis. As you may remember from linear algebra, an orthogonal basis really helps in finding coordinates. In this video you will see why is this basis orthogonal and what  we exactly mean with orthogonality.