# Check Eigenvalues and Eigenvectors are correct [closed]

I have a matrix:

J = {{0, -λ (1 + φ)/τ}, {-(1 + φ)/τ, δ}};


And I compute the Eigenvalues and Eigenvectors as follows:

e = Eigenvalues[J]
v = Eigenvectors[J]


Then I want to check that everything makes sense but this expression returns False. What am I doing wrong?

J.v[[1]] === e[[1]]*v[[1]]

• Try {e, v} = Eigensystem[J] to make sure they are matched. May 27, 2022 at 12:12
• === is for structural equality, == is for mathematical equality. Use the latter. Next time please post copyable code instead of (or in addition to) the image. May 27, 2022 at 12:42
• Try Simplify[J . v[[1]]] === Simplify[e[[1]]*v[[1]]] or ApplySides[Simplify, J . v[[1]] == e[[1]]*v[[1]]]. May 27, 2022 at 12:58

J = {{0, -λ (1 + φ)/τ}, {-(1 + φ)/τ, δ}};

{e, v} = Eigensystem[J];

J . v[[1]] == e[[1]] v[[1]] // FullSimplify
(*    True    *)

J . v[[2]] == e[[2]] v[[2]] // FullSimplify
(*    True    *)

• Thanks. This does it. May 27, 2022 at 12:55
• The point of this answer, @Nicolo, is that if you need both eigenvalues and eigenvectors, you should just use Eigensystem[] at the outset instead of computing them separately. May 27, 2022 at 12:55