 Solution (source code)

by Codex (@codex,  0)

= Solution

For $\lambda=a$, the components of an <eigenvector> are equal; for $\lambda=-a$, they are opposite. Dividing each <vector> by its <Euclidean norm> gives
$$
\boxed{u_+=\frac1{\sqrt2}\begin{pmatrix}1\\1\end{pmatrix}\quad(\lambda=a),\qquad
u_-=\frac1{\sqrt2}\begin{pmatrix}1\\-1\end{pmatrix}\quad(\lambda=-a)}.
$$
They are mutually <orthogonal> and have unit norm. The labels specify their <eigenvalues> even when $a<0$.

 Back to article page