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we have
:<math>A \begin{bmatrix} 1\\0\\0 \end{bmatrix} = \begin{bmatrix} 1\\0\\0 \end{bmatrix} = 1 \cdot \begin{bmatrix} 1\\0\\0 \end{bmatrix},\quad\quad</math>
:<math>A \begin{bmatrix} 0\\0\\1 \end{bmatrix} = \begin{bmatrix} 0\\0\\3 \end{bmatrix} = 3 \cdot \begin{bmatrix} 0\\0\\1 \end{bmatrix}
Therefore, the vectors <math>[1,0,0]^\mathsf{T}</math> and <math>[0,0,1]^\mathsf{T}</math> are eigenvectors of <math>A</math> corresponding to the eigenvalues 1 and 3 respectively. (Here the symbol <math>{}^\mathsf{T}</math> indicates [[transpose of a matrix|matrix transposition]], in this case turning the row vectors into column vectors.)
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