I often read that every tensor of order $2$ can be represented as a matrix (I do understand that). But not every matrix is the representation of some second order tensor. I am not sure, if I understand that correctly. Is it just that any matrix that represents a second order tensor has to be quadratic, i.e. a $n\times n$ matrix?
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2Related: Are matrices and second rank tensors the same thing? and links therein. – Qmechanic Jan 26 '21 at 14:01
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1Where did you read that? It's not really correct. – Javier Jan 26 '21 at 15:04