I have been reading through Chapter 9 of www.deeplearningbbook.org, where convolutional networks are being described.
The following image represents the output of a 2D convolution, without kernel flipping.
The book goes on to describe this matrix as a Toeplitz matrix where,
for univariate discrete convolution, each row of the matrix is constrained to be equal to the row above shifted by one element.
I fully understand this statement since
z are constants in their respective columns with shifting elements.
However, there is no mention of diagonal-constants which are a key feature of such matrices. As per Wikipedia (link above) and several other sources:
a Toeplitz matrix or diagonal-constant matrix, named after Otto Toeplitz, is a matrix in which each descending diagonal from left to right is constant.
Going back to the image above, does this mean that, for instance,
aw == cx == gy? How can this be ensured when all elements are different?