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by chas
2959 days ago
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Similar to how linear transforms can be represented as 2-dimensional arrays of numbers (that is to say matrices)[0], tensors are a higher dimensional analogue with a rich theory in their own right and a representation as higher-dimensional arrays of numbers. Similarly, if you look at a tensor solely as an n-dimensional array of numbers, it ignores important differences in the mathematical behavior of objects with the same representation. To give an example: Different parts of a tensor can behave differently under change of basis. [1] [0] https://www.youtube.com/watch?v=kYB8IZa5AuE [1] https://en.wikipedia.org/wiki/Covariance_and_contravariance_... |
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