$$\begin{bmatrix} 1 & 1 & 0\\ 0 & 1 & 0\\ 0 & 0 & 1 \end{bmatrix}$$ I'm getting 3 eigenvalues 1, 1, 1 (all same) and on solving for eigenvector I'm getting $$\begin{bmatrix} 0 & 1 & 0\\ 0 & 0 & 0\\ 0 & 0 & 0 \end{bmatrix}$$ $x_{2}$=0 how to proceed further?
2026-04-02 10:45:43.1775126743
Eigenvalues and Eigenvectors for the following matrix
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The eigenspace is defined by the single linear equation $x_2$, so it has dimension $2$, and two obvious linearly independent eigenvectors are made up of the first and last column of the matrix. The second column is a generalised eigenvector.