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216
Economic Dynamics
In this instance the output in both programmes is almost identical.
Mathematica
,
however, qualifes the solution For
z[t]
by adding 15
If[t==0,1,0]
.IF
t
is time,
then this will not occur, and so this conditional statement can be ignored, in which
case the two programmes give the same solution – which is also the one provided
on p. 214.
5.4.2
Solving using the Jordan form
In section 5.3 we Found the eigenvalues oF the matrix
A
and used these to fnd
the matrix
V
Formed From the set oF linearly independent eigenvectors oF
A
. The
diagonal matrix
J
=
diag(
λ
1
,...,λ
n
)
(5.6)
is the Jordan Form oF
A
and
V
is the transition matrix, such that
V
−
1
AV
=
J
(5.7)
±rom this result we have
A
t
=
VJ
t
V
−
1
and since the solution to the system
u
t
=
Au
t
−
1
is
u
t
=
A
t
u
0
, then
u
t
=
VJ
t
V
−
1
u
0
where
J
t
=
λ
t
1
0
···
0
0
λ
t
2
0
.
.
.
.
.
.
.
.
.
00
λ
t
n
(5.8)
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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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