Does transfer matrix allows a similarity transformation?

In summary, the transfer matrix is a commonly used tool in condensed matter physics for calculating transmission. The question is whether the transfer matrix can undergo a similarity transformation and still be considered a transfer matrix. This transformation can potentially affect the transmission and has a physical significance. While not an expert in this field, it is known that similar matrices represent the same transformation under different bases. This can be useful in diagonalizing the transfer matrix and analyzing large systems.
  • #1
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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?
 
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  • #2
I'm not quite familiar with condensed matter physics, but I can recall that similar matrices are the same transformation under different basis.
 
  • #3
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).
 

Related to Does transfer matrix allows a similarity transformation?

Question 1: What is a transfer matrix?

A transfer matrix is a mathematical tool used in linear systems and control theory to represent the relationship between input and output variables. It is commonly used in the analysis of dynamical systems and can be used to predict the behavior of a system over time.

Question 2: How is a transfer matrix related to a similarity transformation?

A transfer matrix allows for a similarity transformation to be performed on a system's state space representation. This transformation is used to simplify the analysis of a system by changing the basis of the state space to one that is more convenient for analysis.

Question 3: What is a similarity transformation?

A similarity transformation is a mathematical operation that transforms a matrix into a similar matrix, meaning they have the same eigenvalues. It is commonly used in linear algebra to simplify the analysis of matrices and systems.

Question 4: How is a similarity transformation used in the analysis of systems?

A similarity transformation is used to transform the state space representation of a system into a new basis that is more convenient for analysis. This allows for the system's behavior to be studied in a simpler form, making it easier to understand and predict.

Question 5: Can a transfer matrix be used for nonlinear systems?

Yes, a transfer matrix can be used for both linear and nonlinear systems. However, for nonlinear systems, the transfer matrix may need to be updated at each time step to accurately represent the system's behavior.

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