Small linalg clarifications

tex/linalg/dual-trace.tex

@@ -486,6 +486,11 @@ \section{\problemhead}
 		Follows by writing $T$ in an eigenbasis:
 		then the diagonal entries are the eigenvalues.
 	\end{hint}
+	\begin{sol}
+		We saw already the trace is always the sum of the eigenvalues, in \emph{any} basis.
+		In particular, choosing the Jordan form basis from the previous chapter
+		gives the result because the Jordan form has the eigenvalues for its diagonal entries.
+	\end{sol}
 \end{problem}
 
 \begin{dproblem}

tex/linalg/eigenvalues.tex

@@ -533,6 +533,7 @@ \section{Algebraic and geometric multiplicity}
 	\end{itemize}
 	(Silly edge case: we allow ``multiplicity zero''
 	if $\lambda$ is not an eigenvalue at all.)
+  \label{def:eigen_multiplicity}
 \end{definition}
 However in practice you should just count the Jordan blocks.
 \begin{example}
@@ -566,6 +567,10 @@ \section{Algebraic and geometric multiplicity}
 		corresponding to those blocks.
 	\end{itemize}
 \end{proposition}
+\begin{proof}
+  \Cref{def:eigen_multiplicity} was essentially chosen
+  to be a basis-free rephrasing of this proposition.
+\end{proof}
 
 \begin{ques}
 	Show that the geometric multiplicity