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Diagonal matrix/Eigenspaces/Geometric multiplicity/Exercise
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Determine the
eigenvalues
, the
eigenspaces
, and the
geometric multiplicities
of the matrix
(
2
0
⋯
⋯
⋯
0
0
1
⋱
⋱
⋮
⋮
⋮
⋱
3
⋱
⋱
⋮
⋮
⋱
⋱
1
⋱
⋮
⋮
⋮
⋱
⋱
3
0
0
⋯
⋯
⋯
0
1
)
.
{\displaystyle {\begin{pmatrix}2&0&\cdots &\cdots &\cdots &0\\0&1&\ddots &\ddots &\vdots &\vdots \\\vdots &\ddots &3&\ddots &\ddots &\vdots \\\vdots &\ddots &\ddots &1&\ddots &\vdots \\\vdots &\vdots &\ddots &\ddots &3&0\\0&\cdots &\cdots &\cdots &0&1\end{pmatrix}}.}
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