I was thinking whether the identity matrix could be considered as a rank 2 tensor or not, but then I found out that there is a tensor called identity tensor that has the same function.
So what do you think?
Difference between Identity Matrix and Identity Tensor
matricestensors
Best Answer
A tensor is an object satisfying a certain transformation law relating its components in different coordinate systems. Any tensor which has the same components as the identity matrix in one Cartesian coordinate system also achieves that in all others obtainable by an orthogonal transformation. But more general transformations can have different effects. For example, a Euclidean plane satisfies$$\mathrm{d}s^2=\mathrm{d}x^2+\mathrm{d}y^2=\mathrm{d}r^2+r^2\mathrm{d}\theta^2=g_{ab}\mathrm{d}x^a\mathrm{d}x^b.$$In Cartesian coordinates, the metric tensor's components are those of the identity matrix, viz. $g_{ab}=\delta_{ab}$. In polar coordinates, the matrix we get is $\operatorname{diag}(1,\,r^2)$ instead.