The visualization demonstrates that if we rotate our coordinate system, the vectors $S$ and $T$ transform according to the rules of a vector. For the relationship $T=Q \cdot S$ to remain true in the new coordinate system, the matrix $Q$ must also transform according to the rules of a tensor. This is the essence of the quotient law.
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$\complement\cdots$Counselor
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The quotient law of tensors provides a test for whether a given set of components forms a tensor
The quotient law of tensors provides a test for whether a given set of components forms a tensor
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$\gg$Operations and Properties of Tensors
$\ggg$Mathematical Structures Underlying Physical Laws
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