A chain binomial model is a Markov chain with a transition matrix whose rows are binomial probabilities. Two such chains are presented and illustrated with possible applications. The paper will focus in particular on some interesting properties of the transition matrices.
The eigenvectors and eigenvalues of block circulant matrices had been found
for real symmetric matrices with symmetric submatrices, and for block circulant
matrices with circulant submatrices. The eigenvectors are now found
for general block circulant matrices, including the Jordan Canonical Form
for defective eigenvectors. That analysis is applied to Stephen J. Watson’s
alternating circulant matrices, which reduce to block circulant matrices with
square submatrices of order 2.
