Find a right eigenvector for each distinct eigenvalue

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Reference no: EM13909612

Answer the following questions for the following stochastic matrix [P]:

[P] =

1/2	1/2	0
0	1/2	1/2
0	0	1

(a) Find [Pn] in closed form for arbitrary n > 1.

(b) Find all distinct eigenvalues and the multiplicity of each distinct eigenvalue for [P].

(c) Find a right eigenvector for each distinct eigenvalue, and show that the eigenvalue of multiplicity 2 does not have two linearly independent eigenvectors.

(d) Use (c) to show that there is no diagonal matrix [η] and no invertible matrix [U] for which [P][U] = [U][η].

(e) Rederive the result of (d) using the result of (a) rather than (c).

Text Book: Stochastic Processes: Theory for Applications By Robert G. Gallager.

Reference no: EM13909612

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