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The Vandermonde matrix is a used in the calculation of interpolating polynomials but is more often encountered in the proof that such polynomial interpolates exist. It is also often encountered in the study of determinants since it has a really nice determinant formula. Chapters 0:00 - Introduction 01:01 - Uniqueness 02:30 The Vandermonde Matrix The product links below are Amazon affiliate links. If you buy certain products on Amazon soon after clicking them, I may receive a commission. The price is the same for you, but it does help to support the channel :-) The Approximation Theory series is based on the book "Approximation Theory and Methods" by M.J.D. Powell: https://amzn.to/3CXQpQZ Books used in research for this video: Analysis of Numerical Methods by Isaacson and Bishop Keller - https://amzn.to/31uVljh Linear Algebra and Matrix Theory by Evar D. Nering - No link available. This video was made using: Animation - Apple Keynote Editing - DaVinci Resolve Mic - Blue Yeti X - https://amzn.to/3nJbmdO Supporting the Channel. If you would like to support me in making free mathematics tutorials then you can make a small donation over at https://www.buymeacoffee.com/DrWillWood Thank you so much, I hope you find the content useful.