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How is different a tensor of order 3 or higher from a matrix?

I've read that the first order tensors are vectors and second order tensors are matrices. I have difficulties to understand what a tensor of order 3 looks like. Is it for example a 3-dimensional matrix? That it was my the first thought.

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You can certainly represent an order 3 tensor as a 3-dimenional array of numbers, and you can think of this as being a 3-dimensional equivalent of a matrix (although the term "matrix" is usually taken to mean a 2-dimensional array).

The representation depends on the basis that you choose - and the thing that determines whether a 3-dimensional array is actually a tensor or not is how its values transform when you change your basis.

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  • $\begingroup$ Thank you for your answer. So a 3-dimensional array might be or not be a tensor? Can you please provide an example or a brief explanation when a 3-dimensional array is a tensor and when is not? $\endgroup$
    – Gina
    Commented Oct 6, 2017 at 8:01

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