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## Main Question or Discussion Point

What is a tensor and why is it useful?

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What is a tensor and why is it useful?

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HallsofIvy

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The point of that is: If a tensor has all its components 0 in one coordinate system, then (since we are multiplying all those numbers by the 0 components) it has all components 0 in any coordinate system.

Why is that important? Because coordinate systems are not "natural"- we make them up ourselves- so any equations representing "natural laws" should be independent of the coordinates system. If I can write a "natural law" as A= B where A and B are both tensors, that is the same as A-B= 0. And if that is true in one coordinates system, then it is true in all. That is: if a tensor equation is true in any coordinate system, then it is true in all coordinate systems.

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mathwonk

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young person, there have been approximately 100,000 words written on this question in the last 9 months here. is it possible to search the site on this topic?

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jma2001

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