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4/29/2010
1
Homogeneous Linear
Systems with Constant
Coefficients
Differential Equations
Section 8.2
Eigenvalues and Eigenvectors
Distinct Real Eigenvalues
¢
For each eigenvalue there
corresponds an eigenvector
K
satisfying
and a solution of the form
1
(
)0
A
IK
l
=
1
t
X
Ke
l
=
Repeated Eigenvalues
¢
Case I
– If the coefficient matrix is
symmetric
then you can obtain two
linear independent eigenvectors from
one eigenvalue.
Repeated Eigenvalues
¢
Case II
– If there is only one
eigenvector associated with a
repeated eigenvalue then a second
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 Fall '10
 PamelaSatterfield
 Differential Equations, Eigenvectors, Equations, Vectors, Linear Systems

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