Question

What is a tensor itself?
What is tensor notation used for?

What is differencce between a tensor and a vector?

Answer 1

1] In Physics, we generally deal with Scalars, Vectors and Tensors.

A Scalar is a physical quantity which is described by its magnitude(numeric value). For example temperature.

A Vector is a physical quantity which is described by two things namely magnitude and direction. For example Velocity, acceleration.

A Tensor is physical quantity which is described by three things namely magnitude, direction and the plane of action.(Action Plane) For Example stress is tensor which will have nine components. Assume a 3 * 3 matrix for this. A stress tensor will have magnitude, direction and which plane the component acts on.

2]A tensor of rank (m, n), also called a (m, n) tensor, is defined to be a scalar function of m one-forms and n vectors that is linear in all of its arguments. Tensors will have magnitude and two directions example stress and strain.The second order tensors are symbolized by bold letters.

3]The elements of the tensor are functions of position and the tensor forms which is known as a tensor field. The tensor is defined at every point within a region of space (or space-time), rather than just at a point, or collection of isolated points.Tensors, generally consist of multi-dimensional arrays of numbers, or functions.

A tensor may consist of a single number, where in it is referred to as a tensor of order zero which is a scalar. Tensor of order one is known as a vector.