Linear Algebra and Its Applications · Problem 7.3.4

Computations with Matrices — Gilbert Strang

Mathematics · inverse-power-method-markov

Problem

The Markov matrix

A = \begin{bmatrix} .9 & .3 \\ .1 & .7 \end{bmatrix}

has

\lambda = 1

and

.6

, and the power method

u_k = A^k u_0

converges to

\begin{bmatrix} .75 \\ .25 \end{bmatrix}

. Find the eigenvectors of

A^{-1}

. What does the inverse power method

u_{-k} = A^{-k} u_0

converge to (after you multiply by

.6^k