The CQT toolbox provides a new MATLAB type that represents semi-infinite matrices obtained as the sum of a Toeplitz matrix and a finite-dimensional correction in the top-left corner.
The arithmetic, plus many additional functions, are implemented (or will be included soon) in the toolbox.
To install the latest version in your MATLAB environment you can run the following commands:
unzip('https://github.com/numpi/cqt-toolbox/archive/master.zip'); ...
movefile('cqt-toolbox-master', 'cqt-toolbox'); ...
addpath(fullfile('cqt-toolbox')); savepath;