Finite Dimensional Spaces

This lecture covers the concept of finite dimensional spaces, focusing on the extraction process and the generation of bases. It explains the proposition that if a space is of finite dimension, then another space derived from it is also finite. The lecture delves into the completion process, demonstrating how to complete a space using additional elements. It also discusses the dimension of a space, denoted by 'd', and the properties of bases in relation to the dimension of a space. The presentation concludes with examples of real polynomials and the interpolating Lagrange polynomials.