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Math and science::Algebra
Eigenvalues of a triangular matrix
The eigenvalues of the matrix:
\[\begin{bmatrix}1 & 2 & 5 \\ 0 & 4 & 7 \\ 0 & 0 & 6 \end{bmatrix} \]
are \(1, 4 \) and \( 6\).
This follows from:
\[ \det \begin{bmatrix}1 & 2 & 5 \\ 0 & 4 & 7 \\ 0 & 0 & 6 \end{bmatrix} = (\lambda -1 )(\lambda - 4)(\lambda - 6) =0 \]
This can also be seen by zero-ing the elements of candidate eigenvectors so that the effective matrix loses its later rows.
