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Discrete systems of equations
217
In each of these instructions the last line is a check that undertaking the matrix
multiplication does indeed lead to the Jordan form of the matrix. In each package
we get the Jordan form
J
=
±
10
03
²
However, the transition matrix in each package on the face of it looks different.
More speciFcally,
Mathematica
V
=
±
−
11
²
Maple
V
=
³
1
2
1
2
−
1
2
1
2
´
Butthesearefundamentallythesame.Wenotedthiswhenderivingtheeigenvectors
in the previous section. We arbitrarily chose values for
v
r
1
or
v
r
2
(along with the
values associated with the eigenvalue
s
). In
Maple
, consider the Frst column,
which is the Frst eigenvector. Setting
v
r
2
=
1, means multiplying the Frst term by
−
2, which gives a value for
v
r
1
=−
1. Similarly, setting
v
s
1
=
1in
Maple
, converts
v
s
2
also to the value of unity. Hence, the two matrices are identical. In each case
the last instruction veriFes that
V
−
1
AV
=
J
.
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This note was uploaded on 12/14/2011 for the course ECO 3023 taught by Professor Dr.gwartney during the Fall '11 term at FSU.
 Fall '11
 Dr.Gwartney
 Economics

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