Systems of Frstorder differential equations
159
Figure 4.14.
−
v
s
1
+
v
s
2
=
0 and hence
v
s
=
±
1
1
²
Figure 4.14 illustrates the two eigenvectors associated with the two eigenvalues.
Although this illustration had two distinct roots, it is quite clear that for any
system of two dimensions, there will be two roots that correspond to one of the
following possibilities:
(1)
real and distinct
(2)
real and equal
(3)
complex conjugate.
It is possible to relate these three possibilities to conditions imposed on the trace
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 Fall '11
 Dr.Gwartney
 Economics, Linear Algebra, Characteristic polynomial, Complex number, ad − bc, firstorder differential equations

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