Suppose I had this matrix
$A = \begin{bmatrix} -1 & 0 \\ 0 & 0 \end{bmatrix}$
eigs of $A$ is $-1$, and $0$
What would be the logic in picking the eigenvector for this scenario?
2026-04-09 00:47:36.1775695656
What is the logic behind picking eigenvectors when eigenvalue is zero
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Think about (simple) eigenspaces. The eigenvalue tells you the scaling factor for how that matrix acts on the corresponding eigenspace. (There are some details about generalized eigenvalues that aren't super relevant here) So in the eigenvalue 0 case, the eigenvector tells you what subspace is getting collapsed to the origin.