Understanding of tensor expansion matrices

Tensor of the module expansion matrix, the main task is to reduce the tensor, transformed into a matrix. In the tensor matrix expansion process, is the composition tensor of all orders in staggered order sampling, not simply take a certain order of the eigenvalues in the second order of the eigenvalues, and in the whole process of the different orders of the characteristics of the mixed interleaved sampling, so that in the acquisition process to achieve the tensor of different order between the characteristics of the transfer and fusion.

A (1) matrix is a matrix of i1x (I2XI3) =3x (2x3) =3x6

On the basis of the understanding, plus their own expansion method, along the next module sequence expansion. That is, the two-dimensional column expands.

The following content is from http://blog.csdn.net/keith0812/article/details/20309893

For example, the following:

A is a (4x3x2) third-order tensor.

here is the first-order mode expansion matrix for the third-order tensor a:

the first-order mode expansion matrix of A is a (4x6) matrix, and the 6 columns in the matrix are the second and third-order eigenvalues that are worth interleaving.

second-order mode expansion matrix for third-order tensor a:

the second-order mode expansion matrix of A is a (3x8) matrix.

third-order mode expansion matrix for tertiary tensor a:

the third-order mode expansion matrix of A is a (2x12) matrix.