8_2, Homogeneous Linear Systems with Constant Coefficients

8_2, Homogeneous Linear Systems with Constant Coefficients...

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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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