Eigenvalues—I’m getting wrong result
On pp. 280–281 of the book Solar System Dynamics (), eigenvalues $ g $ and eigenvectors $ \bar e_{ji} $ of matrix $ \mathbf A = \begin{pmatrix} +0.00203738 & -0.00132987 \\ -0.00328007 & +0.00502513 \end{pmatrix} $ (p. 280) are calculated. The results are $ g_1 = 9.63435 \times 10^{-4} $ and $ g_2 = 6.09908 \times 10^{-3} $ (p. 280, which I also get) and $ \bar e = \begin{pmatrix} -0.777991 & 0.332842 \\ -0.628275 & -1.01657 \end{pmatrix} $ (p. 281), or at least the way I understand the problem (I haven’t done matrices in 30+ years, and never did eigenvalues or eigenvectors before now).
I get wholly different results for $ \bar e $, though… $ \begin{pmatrix} -0.35001 & 1.15833 \\ 1 & 1 \end{pmatrix} $, for example, with . These are not even scalable to the values given in the book, so it’s not a matter of multiplying them by a constant…
What am I doing wrong? or misunderstanding?
Thanks in advance for any help!
P.S. There are published errata for this book, e.g. the value of $ S_2\ \text{sin}\ \beta_2 $ at the bottom of p. 281 should be $ -0.0375549 $ instead of $ -0.375549 $, but never any mention of any error in $ \bar e $…
$\endgroup$ 02 Answers
$\begingroup$Maple says $$\overline{e}=\begin{pmatrix} -0.777991219286310 & 0.311162928367653 \\ -0.628275148890516 & -0.950356581504893 \end{pmatrix}$$This is not so far from the book's answer you quote. Another possibility is (after scaling)$$\overline{e}=\begin{pmatrix} 1,2383 & -0.3274 \\ 1 & 1 \end{pmatrix}$$which is close to what you found, if you transpose the matrix (representing vectors in columns and not in line, perhaps..).
$\endgroup$ 17 $\begingroup$From the book___________________________________
On the right hand page, formulas (7.42) show problems.
$$ $$
