User talk:Wenjiajing

Matrix exponential
Hello. I am afraid I had to revert your edit to matrix exponential. I have no idea what you mean with the real-entry canonical form; could you please explain that? But something does seem to be wrong with your example: if
 * $$ B = \begin{bmatrix} 0 & (7+4\sqrt{3})\pi\\ (-7+4\sqrt{3})\pi & 0 \end{bmatrix} $$

then
 * $$ \exp(B) = \begin{bmatrix} \cosh\pi & (7+4\sqrt{3})\sinh\pi\\ (7-4\sqrt{3})\sinh\pi & \cosh \end{bmatrix} $$

which is not the identity matrix as you claim. It looks like some signs are wrong: if you replace $$-7+4\sqrt{3}$$ by $$7-4\sqrt{3}$$ in the matrix B, then its exponential is minus the identity. -- Jitse Niesen (talk) 12:12, 29 October 2008 (UTC)

ture! It should be $$7-4\sqrt{3}$$. Thanks. By real-entry canonical form, I mean a canonical form that contains real-entries only. Then the diagonal block corresponding to a pair of complex conjugate eigenvalues won't be diagonal matrix but of the form :$$ \begin{bmatrix} \alpha & \beta \\ -\beta & \alpha \end{bmatrix} $$ where $$\alpha \pm \beta i$$ will be the eigenvalues. - Wenjiajing (talk) 19:59, 2 March 2009 (UTC)