Note: This page has been translated by MathWorks. Please click here

To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.

To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.

Plot Markov chain eigenvalues

`eigplot(mc)`

`eVals = eigplot(mc)`

`[eVals,hz] = eigplot(mc)`

`eigplot(`

creates a plot of the
eigenvalues of the transition matrix of the discrete-time Markov chain
`mc`

)`mc`

on the complex plane. The plot highlights:

The unit circle

The Perron-Frobenius eigenvalue at (1,0)

The circle of second largest eigenvalue magnitude (SLEM)

the spectral gap between the two circles, which determines the mixing time

[1]
Gallager, R.G. *Stochastic Processes: Theory for Applications.* Cambridge, UK: Cambridge University Press, 2013.

[2]
Horn, R. and C. R. Johnson. *Matrix Analysis.* Cambridge, UK: Cambridge University Press, 1985.

[3]
Seneta, E. *Non-negative Matrices and Markov Chains.* New York, NY: Springer-Verlag, 1981.

Was this topic helpful?