- #1
Somefantastik
- 226
- 0
finding the eigenvectors (and behavior of solution) around the critical points found in this thread: https://www.physicsforums.com/showthread.php?t=258349&referrerid=110346
D_{f} = \[\begin{pmatrix}32x & 18y \\ 32x & -32y\end{pmatrix}\]
D_{f}(1,1) = \[\begin{pmatrix}32 & 18 \\ 32 & -32\end{pmatrix}\]
= \[\begin{pmatrix}16 & 9 \\ 16 & -16 \end{pmatrix}\]
det(A-\lambda I) =\[\begin{pmatrix} 16-\lambda & 9 \\ 16 & -16- \lambda \end{pmatrix}\]
= -256 + \lambda^{2} - 146 \ => \ \lambda = ^{+}_{-}20
\lambda_{1} = 20:
(A-\lambda_{1} I)\xi^{(1)} = 0 \ => \ \[\begin{pmatrix} -4 & 9 \\ 16 & -36 \end{pmatrix}\]\xi^{(1)} = 0
I can't get LaTeX to cooperate with me, that's supposed to say [-4 9; 16 -36]ξ(1) = 0
=> \ \xi^{(1)} = \left[^{9}_{4} \right]
Having trouble finding \xi^{(2)} when \lambda_{2} = -20.
Keeps coming out to be [0 0]T.
Any suggestions?
D_{f} = \[\begin{pmatrix}32x & 18y \\ 32x & -32y\end{pmatrix}\]
D_{f}(1,1) = \[\begin{pmatrix}32 & 18 \\ 32 & -32\end{pmatrix}\]
= \[\begin{pmatrix}16 & 9 \\ 16 & -16 \end{pmatrix}\]
det(A-\lambda I) =\[\begin{pmatrix} 16-\lambda & 9 \\ 16 & -16- \lambda \end{pmatrix}\]
= -256 + \lambda^{2} - 146 \ => \ \lambda = ^{+}_{-}20
\lambda_{1} = 20:
(A-\lambda_{1} I)\xi^{(1)} = 0 \ => \ \[\begin{pmatrix} -4 & 9 \\ 16 & -36 \end{pmatrix}\]\xi^{(1)} = 0
I can't get LaTeX to cooperate with me, that's supposed to say [-4 9; 16 -36]ξ(1) = 0
=> \ \xi^{(1)} = \left[^{9}_{4} \right]
Having trouble finding \xi^{(2)} when \lambda_{2} = -20.
Keeps coming out to be [0 0]T.
Any suggestions?
