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## Main Question or Discussion Point

Hello i have this matrix [itex]\in Z [/itex] mod [itex] 7[/itex],

M = \begin{pmatrix} 0&6\\ 5&0 \end{pmatrix}

always modulo [itex]7[/itex] in [itex]Z[/itex].

I found characteristic polynomial [itex]x^2+5[/itex].

Eigenvalues are [itex]\lambda = 3, \lambda' = 4[/itex]

Eigenvectors related to [itex]\lambda = 3 [/itex] are the non-zero solution of the system:

[itex]4x +6y = 0,[/itex]

[itex]5x+4y = 0 [/itex]

I get:

[itex]4x = y,[/itex]

[itex]6y[/itex]

I don't know if it is correct, but how can i find the eigenvectors?

M = \begin{pmatrix} 0&6\\ 5&0 \end{pmatrix}

always modulo [itex]7[/itex] in [itex]Z[/itex].

I found characteristic polynomial [itex]x^2+5[/itex].

Eigenvalues are [itex]\lambda = 3, \lambda' = 4[/itex]

Eigenvectors related to [itex]\lambda = 3 [/itex] are the non-zero solution of the system:

[itex]4x +6y = 0,[/itex]

[itex]5x+4y = 0 [/itex]

I get:

[itex]4x = y,[/itex]

[itex]6y[/itex]

I don't know if it is correct, but how can i find the eigenvectors?