Orthogonal Projection: Euclidean Space

This lecture covers the concept of orthogonal projection in a Euclidean space, where a vector is uniquely decomposed into two components: one lying in a given subspace and the other orthogonal to it. The instructor explains how to calculate the orthogonal projection, emphasizing its uniqueness and dependence on the choice of subspace. The lecture also delves into finding orthonormal bases, least squares solutions, and properties of matrices in relation to orthogonal projections.