# Question:How to calculate Eigenvector of a symbolic matrix in Maple?

## Question:How to calculate Eigenvector of a symbolic matrix in Maple?

Maple

I am rather new to using maple so I'm not super familiar with the syntax and sometimes get confused with some of my output. With that said, I am trying to derive some equations symbolically that can later be computed in Fortran. This requires that I find the Eigenvectors of a symbolic 5×5 matrix. I computed the eigenvalues with little problem, however, I cannot seem to compute the Eigenvectors with Maple (not sure if its a syntax issue or what). Here is my code where I am trying to determine the Eigenvectors of A. Any help and advice is appreciated.

E := [q2, q2^2/q1+(gamma-1)*(q5-(1/2)*q2^2/q1-(1/2)*q3^2/q1-(1/2)*q4^2/q1), q2*q3/q1, q4*q2/q1, q5*q2/q1+q2*(gamma-1)*(q5-(1/2)*q2^2/q1-(1/2)*q3^2/q1-(1/2)*q4^2/q1)/q1, q6*q2/q1]

F := [q3, q2*q3/q1, q3^2/q1+(gamma-1)*(q5-(1/2)*q2^2/q1-(1/2)*q3^2/q1-(1/2)*q4^2/q1), q4*q3/q1, q5*q3/q1+q3*(gamma-1)*(q5-(1/2)*q2^2/q1-(1/2)*q3^2/q1-(1/2)*q4^2/q1)/q1, q6*q3/q1]

G := [q4, q4*q2/q1, q4*q3/q1, q4^2/q1+(gamma-1)*(q5-(1/2)*q2^2/q1-(1/2)*q3^2/q1-(1/2)*q4^2/q1), q5*q4/q1+q4*(gamma-1)*(q5-(1/2)*q2^2/q1-(1/2)*q3^2/q1-(1/2)*q4^2/q1)/q1, q6*q4/q1]

Ebar := expand(E*xi_x+F*xi_y+G*xi_z)

U := [q1, q2, q3, q4, q5, q6]

with(VectorCalculus);
A := subs(q1 = rho, q2 = rho*u, q3 = rho*v, q4 = rho*w, q5 = rho*e, q6 = rho*nu, Jacobian(Ebar, U));

A := subs(e = P/((gamma-1)*rho)+(1/2)*u^2+(1/2)*v^2+(1/2)*w^2, A)

A := subs(P = rho*c^2/gamma, A)

A := simplify(A)

with(LinearAlgebra);
EigA := simplify(Eigenvalues(A));

with(LinearAlgebra);
EigenVectorA = Eigenvectors[A];

I have tried specifying which eigenvalue to take the eigenvector with respect to also with different synaxes but none seem to work. I am not claiming the last line of code should be correct, but am looking for how to make it correct. Sorry if I left out any information and thank you so much for your suggestions.

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