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A tensor is a mathematical object (system of functions[1]) that obeys (its components) a law of transformation between two systems of reference (through its direction cosines ) . Certainly, a tensor can be expressed like an array but all array is not necessarily a tensor and this observation is fundamental in the definition of a tensor.

[1] Green, A.E. and Zerna, W., Theoretical Elasticity, p.4, Oxford University Press (1968).

the image and the object represented by the image ARE not the same thing...

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