How to represent a bivector/bi-covector or more complex tensors (of rank 1,2/2,1/2,2 or even higher) using numbers?

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If I understand correctly, the rank 0,0 tensor is just a scalar, rank 0,1 tensor is a vector represented as a column, rank 1,0 is a covector represented as a row, rank 1,1 is a linear transformation represented as a matrix. However, if the linear transformation is represented as a two-dimensional array m * n, then I have no idea how to represent, say, a bivector (or tri- and higher rank) in numerical form, nothing comes to my mind, except as other two-dimensional arrays.