ยง An elementary example of a thing that is not a vector
Consider the tripe (temperature, pressure, humidity) at a point. If we rotate
the picture by 60 degrees, the triple does not change .
Now consider the direction of wind at a point. If we rotate the picture by
60 degrees, the components of the wind vector change with our rotation.
Thus:
a vector is something that transforms like a vector.
To be more precise, I can phrase it as:
A vector iss (is and only is) something that transforms like a vector.
Generalization to tensors is left as an exercise for the reader.