diff --git a/eigenvaluesAndEigenvectors/definition.tex b/eigenvaluesAndEigenvectors/definition.tex index 6644548..1277684 100644 --- a/eigenvaluesAndEigenvectors/definition.tex +++ b/eigenvaluesAndEigenvectors/definition.tex @@ -21,7 +21,7 @@ Before proceeding with examples, we note that -\begin{proposition} If $\bf v$ is an eigenvalue of a matrix $A$, the eigenvector associated with it is unique. +\begin{proposition} If $\bf v$ is an eigenvector of a matrix $A$, the eigenvalue associated with it is unique. \end{proposition} \begin{proof} Suppose $\lambda_1{\bf v} = A*{\bf v} = \lambda_2{\bf v}$. Then $\lambda_1{\bf v} - \lambda_2{\bf v} = (\lambda_1 - \lambda_2){\bf v} = {\bf 0}$. But since ${\bf v}\ne {\bf 0}$, the only way this could happen is if the coefficient $(\lambda_1 - \lambda_2)$ is equal to zero, or equivalently, if $\lambda_1 = \lambda_2$.