Is the identity matrix a tensor?

Question

If we multiply the identity matrix by any vector or a matrix, then the result is the vector or the matrix themselves (like a mirror).

Tensors represent physical quantities, so if it wasn't a physical quantity then it is not a tensor. Right?

What about identity matrix, is it considered to be a tensor? Maybe not because it is an operation not a physical quantity. But there is a tensor that represents it which is the Kronecker delta.

Is the information that I wrote true? I'm trying to understand more about tensors.

Answer 1

The way I understand it as an engineer, not a mathematician:

A second order tensor has the form of a 2-d matrix. The identity matrix is a 2-d matrix with specific values. Under certain circumstances, the identity matrix can represent a 2d order tensor.

Since, the above won't answer your question about understanding what a tensor I would suggest the following two links as starting points (if you haven't followed them already):

• NASA Report - An Introduction to Tensors for Students of Physics and Engineering
• 12 min video, its simplistic yet incredibly intuitive