Uniqueness of Interpolation Polynomials

This lecture discusses the uniqueness of interpolation polynomials, focusing on the scenario where two polynomials of the same degree interpolate the same data points. The instructor explains the conditions under which the interpolation polynomials are unique and explores the concept through various examples. The lecture also covers the Vandermonde matrix and its role in interpolation. Additionally, the instructor introduces the interpolant of a function at given nodes and explains how it is denoted. The lecture concludes with a detailed explanation of the uniqueness of interpolation polynomials and the significance of distinct data points in the interpolation process.