Triangulation of Matrices and Linear Maps

Rami Shakarchi

Chapter Chapter X in Solutions Manual for Lang’s Linear Algebra, 1996, pp 156-159 from Springer

Abstract: Abstract Let A be an upper triangular matrix: $$ A = \left( {\begin{array}{*{20}c} \hfill {a_{11} } & \hfill {a_{12} } & \hfill \ldots & \hfill {a_{1n} } \\ \hfill 0 & \hfill {a_{22} } & \hfill \ldots & \hfill {a_{2n} } \\ \hfill : & \hfill : & \hfill {} & \hfill : \\ \hfill 0 & \hfill 0 & \hfill \ldots & \hfill {a_{nn} } \\ \end{array} } \right). $$ Viewing A as a linear map, what are the eigenvalues of A2, A3 in general Ar where r is an integer ≥1?

Date: 1996
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DOI: 10.1007/978-1-4612-0755-9_10

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