Solution
= Solution
An <eigenvalue equation> has the form $A\mathbf a=\lambda\mathbf a$, where $\mathbf a\ne0$ is an <eigenvector> and $\lambda$ its <eigenvalue>. It means that the <linear map> preserves the vector's line and acts there by multiplication by $\lambda$. Nonzero solutions occur precisely when $\det(A-\lambda I)=0$; the zero vector is excluded because it would satisfy the equation for every $\lambda$.