[Math] What are “cyclic” and “difference” matrices

Question

I'm reading Gilbert's linear algebra book and there is an emphasis on difference (backward and forward according to the book) and cyclic matrices (it says that cyclic matrices don't have inverses, I didn't grasp that too). But I did not quite understand anything about them. Can someone explain it to a newcomer to the subject?

Answer 1

Cyclic, or circulant matrices are matrices of the following form. So the rows and colums are obtained by cyclical permutation. Since the zero matrix and the identity matrix are cyclic, such matrices may or may not be invertible.

Link: Wikipedia.