This proof illustrates that the matrix P = A(ATA)^-1AT serves as the projection matrix for projecting onto a k-dimensional subspace M of R^n. It demonstrates that for any vector m in M, Pm = m. Additionally, for any vector w in R^n, Pw is in M, and for any vector w in R^n, the difference w - Pw is orthogonal to any vector in M. This is part of the Mathematics for Computation and Data Science course (MATH E-23c) in the Spring 2024 term at Harvard. The course covers discrete mathematics, real analysis, linear algebra, and integral calculus, with applications in computer science, probability, statistics, and data science, and also includes an introduction to R programming.
Presented by: Jimmy Q. Tran