B. Dodson
Week 12:
Finish suggested homework 10,
. . .
Graded Homework 12:
Section 3.7  2, 4; and 4.6  7, 11,
pg. 356; due Wed. Dec. 5
From 4.6 we will ONLY cover pp. 322326 (Markov
chains) and pp. 327329 (population growth).
—————
Finally, we’ve gone over the text’s Example 3.46 from
Section 3.7, pp. 228231 and discussed Examples 3.65 and 3.66.
In each case we have an initial state vector
±x
0
and
then subsequent states
±x
1
, ±x
2
, . . . , ±x
k
, . . .
The states are related by a transition probability matrix
P
(or by a Leslie matrix
L
) with
±x
i
=
P±x
i

1
,
so
±x
i
=
P
i
±x
0
(or the same equations with
P
replaced by
L
). In each case we get a steady state
given by an eigenvector of the matrix. For the cases that
occur in the applications the matrix
P
can be diagonalized;
resp. we only need the positive eigenvalue,
and we determine the steady state (resp. rate).
Finally, we recall (below) that we have observed that the material of 4.4
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 Spring '08
 Dodson
 Linear Algebra, Eigenvectors, Matrices, Markov Chains, Eigenvalue, eigenvector and eigenspace, Orthogonal matrix, transition probability matrix

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