Topics in Linear Algebra - The Functional Calculus  - 03 - Polynomial interpolation
Channel: Arthur Parzygnat
Date: 2019-10-06

We finish our example of computing the square-root of a positive 2 by 2 matrix via polynomial interpolation. We then generalize the idea of polynomial interpolation to n points (which is suitable for eigenvalues of n by n matrices). The Vandermonde matrix shows up naturally in trying to solve this problem. There are many ways to solve the polynomial interpolation problem (some easier than this approach), but I wanted to supply a linear algebra method.

This is part of a series of lectures on special topics in linear algebra https://www.youtube.com/playlist?list=PLSx1kJDjrLRSS4Aio9WfQlNnH6X6pC_8t. It is assumed the viewer has taken (or is well into) a course in linear algebra. Some topics may also require additional background. Topics covered include linear regression and data analysis, ordinary linear differential equations, differential operators, function spaces, category-theoretic aspects of linear algebra, support vector machines (machine learning), Hamming's error-correcting codes, stochastic maps and Markov chains, tensor products, finite-dimensional C*-algebras, algebraic probability theory, completely positive maps, aspects of quantum information theory, and more.

The next video on Special Topics in Linear Algebra is on The determinant of a Vandermonde matrix: https://youtu.be/xjDN9kI_qlc

The previous video on Special Topics in Linear Algebra is on Square-root of a positive matrix via an example: https://youtu.be/HhfOipRpAIE

These videos were created during the 2019 Spring/Summer semester at the UConn CETL Lightboard Room.