Based on the properties of

stochastic matrix and Gershgorin disk theorem, except for one eigenvalue [lambda] = 1, all the other eigenvalues satisfy [absolute value of [lambda]] < 1.

or -]] is a

stochastic matrix if p [greater than or equal to] 1 and [[([+ or -]b) - 1]/p] [member of] Z.

Let A be a

stochastic matrix on the state space S and [C.

SSD]r'w if and only if there exists a double

stochastic matrix P = [{[p.

These data served as a basis for the population of the

stochastic matrix of transition probabilities for bulk terminal behaviour (see matrix (6)).

i,j=1,2,3], where [GAMMA] is row stochastic, into a new

stochastic matrix.

H] the |A| x |A| [|H| x |H|]

stochastic matrix which is implied by the transition probabilities defined above.

In [6], the authors present an algorithm for uncoupling a

stochastic matrix that relies on the singular value decomposition of that matrix, rather than the spectral decomposition.

Do this for all entries of C and turn the result into the (6 x 6)

stochastic matrix A", i.

Instead of clustering around the Perron-Frobenius eigenvalue, the reducing eigenvalues of a block

stochastic matrix is separated by a large distance to the origin in the complex plane; see Figure 5.

Let p be a positive integer and B an irreducible column

stochastic matrix with spectral decomposition

Given a

stochastic matrix B representing some states of a biomolecule, but including some noise due to measurements, find a permutation P so that [P.