Topics in Linear Algebra - The Functional Calculus - 04 - The determinant of a Vandermonde matrix

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 • Special Topics in Line... . 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: • Topics in Linear Algeb...
The previous video on Special Topics in Linear Algebra is on Polynomial interpolation: • Topics in Linear Algeb...
These videos were created during the 2019 Spring/Summer semester at the UConn CETL Lightboard Room.

[@Gritpawa]

Concise but yet clear explanation,hats off!!

[@avaciprin492]

how does he write on the back of it but it's legible from the front. is he mirroring his writing or what

[@masteroogwaysballsack5068]

bruh, exactly what i'm wondering

[@0furkanyalcin0]

thank you teacher

[@pavanvadrevu6912]

Thank you so much. This helped me prove the general case.

[@FloThePro1231]

where do you go n->n+1 for induction?

[@paulanjeru1043]

Thank you so much for this! It really helped me understand the proof :)

[@jchord8314]

Big thank from Indonesia🙂
Usefull

[@azharnafis3914]

Much loves from India

[@bonsummers2657]

What's the purpose of this?

[@ArthurParzygnat]

Thank you for your question. I believe the answer is contained in the description to this video: "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." Does this answer your question?

[@ArthurParzygnat]

I should mention there are several other usages of the Vandermonde matrix, but this is the application I have in mind.

[@bonsummers2657]

@@ArthurParzygnat Ok, thank you for the explanation.

[@ArthurParzygnat]

@@bonsummers2657 You're welcome!