 The "order" of a tensor is the number of directions contained within, which is separate from the dimensions of the individual directions.A second-order tensor in two dimensions might be represented mathematically by a 2-by-2 matrix, and in three dimensions by a 3-by-3 matrix, but in both cases the matrix is "square" for a second-order tensor.A third-order tensor has three magnitudes and directions, and would be represented by a cube of numbers, 3-by-3-by-3 for directions in three dimensions, and so on.