What exactly are tensors? | Tensor algebra episode 5

#tensors #tensoralgebra #covariance #contravariance #dualvectors Access exclusive content on Patreon: https://www.patreon.com/user?u=86649007 Tensors are linear functions with more than 1 input. But we can also treat them as functions with only a single input, by just sticking all the inputs together into a bigger object, using tensor glue. We talk about nested tables, and how to transform a tensor to a new basis. We also give you some hints about the confusing index placement and Einstein notation, in case you want to study tensors more deeply. [EIGEN 1]    • Tensors for Beginners   The best way to learn more about tensors and how they transform, is to watch the Youtube playlist by Eigenchris. It's amazing. I can't recommend it enough. 0:00 The goals of this video 1:07 Tensors are multi-linear functions 2:17 Examples of tensors 7:08 First goal: From multi-input to single input 9:40 How do tensors transform under a change of basis? 11:54 Contractions produce basis-independent values 14:41 Finite Fourier analysis, type theory, and more 15:24 Jargon, notation, and confusion This video is published under a CC Attribution license ( https://creativecommons.org/licenses/... )