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Upper triangular matrix/Eigenvalues/Exercise
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Let
M
=
(
d
1
∗
⋯
⋯
∗
0
d
2
∗
⋯
∗
⋮
⋱
⋱
⋱
⋮
0
⋯
0
d
n
−
1
∗
0
⋯
⋯
0
d
n
)
{\displaystyle {}M={\begin{pmatrix}d_{1}&\ast &\cdots &\cdots &\ast \\0&d_{2}&\ast &\cdots &\ast \\\vdots &\ddots &\ddots &\ddots &\vdots \\0&\cdots &0&d_{n-1}&\ast \\0&\cdots &\cdots &0&d_{n}\end{pmatrix}}\,}
be an
upper triangular matrix
. Show that an
eigenvalue
of
M
{\displaystyle {}M}
is a diagonal entry of
M
{\displaystyle {}M}
.
Create a solution