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Nicolae Coculescu
2007 Nicolae Coculescu
1
Matrices A s.t. tr(A)=tr(A²)=0
Matrices A s.t. tr(A)=tr(A²)=0
Source:
December 13, 2019
linear algebra
matrix
Problem Statement
Let
K
\mathbb{K}
K
be a field and let be a matrix
M
∈
M
3
(
K
)
M\in\mathcal{M}_3(\mathbb{K} )
M
∈
M
3
(
K
)
having the property that
tr
(
A
)
=
tr
(
A
2
)
=
0.
\text{tr} (A) =\text{tr} (A^2) =0 .
tr
(
A
)
=
tr
(
A
2
)
=
0.
Show that there is a
μ
∈
K
\mu\in \mathbb{K}
μ
∈
K
such that
A
3
=
μ
A
A^3=\mu A
A
3
=
μ
A
or
A
3
=
μ
I
.
A^3=\mu I.
A
3
=
μ
I
.
Cristinel Mortici
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