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I have recently started reading some notes on introduction to tensors, trying to get more familiar with this mathematical object. I have two questions I can't seem to answer myself:

1. A tensor is roughly defined in the text as a collection of quantities associated with a point in space, which transform according to an unchanging rule. What is meant by

*an unchanging rule*? what exactly is NOT changing?

The following is how I answered to myself: an unchanging rule is a rule according to which the "collection of quantities" is transformed between coordinate systems, without changing the "collection of quantities" or the way it may be interpreted in each coordinates system. Am I right?

2. One line in the text states that "while every rank-0 tensor is a scalar, not every scalar is a rank-0 tensor". temperature is a clear example of a scalar quantity that can be considered a rank-0 tensor, but I could not think of any example for a scalar that is NOT a rank-0 tensor. Could someone please provide one?

Many thanks!