Very easy…
If you use the n-mode product as in the link above, then: 1) OT can have dimensions 2×M×M or M×2×M or M×M×2; 2) R=OTDO cannot be a matrix (i.e., to be an M×M×1 or M×1×M or 1×M×M) tensor.
The multiplication of a tensor by a matrix (or by a vector) is called n-mode product.
Let T∈RI1×I2×⋯×IN be an N-order tensor and M∈RJ×In be a matrix. The n-mode product is defined as
(T×nM)i1⋯in−1jin+1⋯iN=∑in=1InTi1i2⋯in⋯iNMjin.
Note this is not a standard product like the product of matrices. However, you could perform a matricization of the tensor along its n-mode (dimension n) and thus effectuate a standard multiplication.
The n-mode matricization of T, say T(n), is an In×I1⋯In−1In+1⋯IN matrix representation of T. In other words, it is just a matrix form to organize all the entries of T. Hence, the multiplications below are equivalent
Y=T×nM⟺Y(n)=MT(n),
where Y(n) is the n-mode matricization of the tensor Y∈RI1×⋯×In−1×J×In+1×⋯×IN.
For more details, see Tensor Decompositions and Applications.
http://citeseerx.ist.psu.edu/viewdoc/download;jsessionid=4A0663C7848627DADDBA6A243BC43E78?doi=10.1.1.130.782&rep=rep1&type=pdf
너 이 시키 다음엔 제목에 텐서 넣어라. 안 그럼 죽는다잉?