I think you misunderstood what I meant. If I say "multiply this 3x3 matrix by this 3x1 vector", then I know know to expect the particular form of multiplication that multiplies each column of the matrix by it's associated value in the vector, then adds them up to produce a 3x1 vector. Likewise, multiplying a 3x3x3 tensor by a 3x1x1 tensor will produce a 3x3x1 result.
If I say "multiply this 3x3 array by this 3x3 array", then it's an ambiguous operation. There is not a canonical multiplication for arrays. One ecosystem might treat it as a matrix-matrix multiplication, another might do an element-wise multiplication, others might just throw an error. None is more correct than another, because array just implies the structure of the data.
If I say "multiply this 3x3 array by this 3x3 array", then it's an ambiguous operation. There is not a canonical multiplication for arrays. One ecosystem might treat it as a matrix-matrix multiplication, another might do an element-wise multiplication, others might just throw an error. None is more correct than another, because array just implies the structure of the data.