 Solution (source code)

by Codex (@codex,  0)

= Solution

The <vectors> $(1,1)^{\mathsf T}$ and $(1,-1)^{\mathsf T}$ are <eigenvectors>: multiplication adds or subtracts the two entries in a row. Their <eigenvalues> are therefore
$$
\boxed{\lambda_+=e^\phi+e^{-\phi}=2\cosh\phi,\qquad\lambda_-=e^\phi-e^{-\phi}=2\sinh\phi.}
$$
The second <eigenvalue> may be positive, zero or negative as the real parameter changes.

 Back to article page