Does transfer matrix allows a similarity transformation?

[PRB147]

transfer matrix is frequently used in condensed matter physics for the calculation of
the transmission. My question is does the transfer matrix can be made a similarity transformation?
After transformation, is it still be a transfer matrix? does the transformation influence the transmission?
what is the physical significance after transformation?

 

[kof9595995]

I'm not quite familiar with condensed matter physics, but I can recall that similar matrices are the same transformation under different basis.

 

[xepma]

Yea, it's just a change of basis and it is allowed by the transfer matrix. Useful, for instance, to diagonalize the transfer matrix, and to extract the behavior for large systems (large system size means lots of copies of the transfer matrix. In turn, the largest eigenvalue tends to dominate the behavior).