# How to check the stability condition for matrix?

I have a code that in it I need to check the stability condition. These condition induces that my 6*6 matrix have real negative eigenvalues. I want to check that if all of the real eigenvalues for each j are negative, keep these answer as stable if not kept as not stable. how can I do that?

``````A = ( {
{-(Kappa)/2, (CapitalDelta)c(j), -G(j)*Po(j), 0, 0, 0},
{-(CapitalDelta)c(j), -(Kappa)/2, G(j)*Qo(j), 0, 0, 0},
{0, 0, 0, (CapitalOmega)m, 0, 0},
{G(j)*Qo(j), G(j)*Po(j), -(CapitalOmega)mm(j), -(Gamma)m,
Sqrt(2)*gw*Qw, Sqrt(2)*gw*Pw},
{0, 0, -Sqrt(2)*gw*Pw, 0, -(Kappa)w/2, (CapitalDelta)w(j)},
{0, 0, Sqrt(2)*gw*Qw, 0, -(CapitalDelta)w(j), -(Kappa)w/2}
} );
``````

I have these matrix that all parameters are fix and it is the answer of numerical solve for each j. I create eigenvalues by these

``````Re(Eigenvalues(A));
egn1 = Re(Eigenvalues(A)((1))) < 0;
egn2 = Re(Eigenvalues(A)((2))) < 0;
eng3 = Re(Eigenvalues(A)((3))) < 0;
eng4 = Re(Eigenvalues(A)((4))) < 0;
eng5 = Re(Eigenvalues(A)((5))) < 0;
eng6 = Re(Eigenvalues(A)((6))) < 0;
``````

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