The meaning of a tensor, page 1

Dear Friends,

I had another epic discussion with a friend that i know for years, and i have decided to point it out in this tread since it is a good idea to clear up some misunderstandings about the tensors.

My friend has studied electrical engineering, and although the course and the whole subject is at least very challenging, and of course this is one of the most respectful academic schools, i will try to give an overview of the meaning of tensors, since the teaching in the above department has been dramatically decreased in terms of quality the last 10 years.

My friend asked me what is a tensor, and what is the physical meaning of a tensor. The answer is quite simple, but plenty of care should be taken if we are about to define such a quantity

A tensor is a mathematical tool, although it stands also as a geometrical entity itself, that transforms according to certain rules under a change of co-ordinates.

The properties of a physical system could be characterised by tensors, the whole of Einstein's Theory of relativity is based on tensors.

The tensor can either be a point in space-time (scalar) that is called tensor with order zero or

Two or more points in space-time (vectors) that is called a tensor with order one or

A matrice that is called a tensor with order two

Therefore a tensor transforms from one vector to another, and this is independent of the frame of reference.

Or a tensor trasforms a particular set of co-ordinates (x,y,z) to another set of co-ordinates under the rules govern the system

For example if you apply a force F to a moving object then the object will accelerate, to a different direction from the direction you applied the force, unless the force acts on the same direction with the moving object. The shape of the object is also important regarding the direction of acceleration.

Therefore the tensor transforms from one vector (the force) to another vector (the accelaration).

Thanks,

TN1