Topics in Linear Algebra - The Functional Calculus  - 04 - The determinant of a Vandermonde matrix
Channel: Arthur Parzygnat
Date: 2019-10-06

We compute the determinant of a Vandermonde matrix. We do this inductively by Gaussian elimination. This is an intermediate step in trying to find a polynomial that interpolates several points, which itself is used for computing f(A) for a function f defined on the eigenvalues of the matrix A. 

Note: somewhere around 6:05, I keep saying you get lambda_2 -lambda_3, but I mean lambda_3 - lambda_2.

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 a Proof of the main theorem for the functional calculus: https://youtu.be/CDNvJnNKySQ

The previous video on Special Topics in Linear Algebra is on Polynomial interpolation: https://youtu.be/7_RB9TLSWpc

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