What exactly are tensors? | Tensor algebra episode 5

Описание: #tensors #tensoralgebra #covariance #contravariance #dualvectors

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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

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