An Introduction To Tensors for Students of Physics and Engineering
Joseph C. Kolecki National Aeronautics and Space Administration Glenn Research Center NASA/TM-2002-211716
Tensors are typically defined by their coordinate transformation properties. The transformation properties of tensors can be understood by realizing that the physical quantities they represent
must appear in certain ways to different observers with different points of view.Suppose, for example, that I measure the temperature (°C) at a given point P at a given time. You also measure the temperature (°C) at P at the same time but from a different location that is in motion relative to my location. Would it make any sense if you and I acquired different magnitudes; i.e., if my thermometer measured 25°C and yours measured 125°C? No. We must both obtain the same quantity from our respective measurements.Put another way, suppose that I call my point of view (coordinate system or reference frame) K and yours K*. Let T be the temperature (°C) measured at P in K and T* be the temperature (°C)
measured in K*. We then require T = T*."