A tensor is often thought of as a generalized matrix. That is, it could be a 1-D matrix (a vector is actually such a tensor), a 3-D matrix (something like a cube of numbers), even a 0-D matrix (a single number), or a higher dimensional structure that is harder to visualize. The dimension of the tensor is called its rank. - What’s the difference between a matrix and a tensor?

But this description misses the most important property of a tensor!

Any rank-2 tensor can be represented as a matrix, but not every matrix is really a rank-2 tensor. The numerical values of a tensor’s matrix representation depend on what transformation rules have been applied to the entire system.

The bottom line of this is:

• The components of a rank-2 tensor can be written in a matrix.
• The tensor is not that matrix, because different types of tensors can correspond to the same matrix.
• The differences between those tensor types are uncovered by the basis transformations (hence the physicist’s definition: “A tensor is what transforms like a tensor”).