A meaningful decomposition of an infinite order matrix.

[Hongyi Zhao <hongyi.zhao@gmail.com>]

Hi here,

I've the following matrix, whose order is infinity:

[ 0, 0, 1; 0, 1, 0; 1, 0, 1 ]

In addition, this matrix is obtained the product of the following two
matrices whose orders are finite:

[[0, 0, -1; 0, 1, 0; 1, 0, 1]; [1, 0, 2; 0, 1, 0; 0, 0, -1]]

I would like to know if it is possible to reverse the above process,
i.e., decompose an infinite-order matrix into a product of
finite-order matrices with intuitive meanings from a geometric,
mathematical, or physical point of view.

Regards,
Zhao
-- 
Assoc. Prof. Hongsheng Zhao <hongyi.zhao@gmail.com>
Theory and Simulation of Materials
Hebei Vocational University of Technology and Engineering
No. 473, Quannan West Street, Xindu District, Xingtai, Hebei province