Eigenvalues & Eigenvectors
Find eigenvalues and eigenvectors from the characteristic polynomial, with det(A − λI) = 0 expanded and each eigenvector solved. Try “eigenvalues of [[4,1],[2,3]]”.
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What you can do with the Eigenvalues & Eigenvectors
Characteristic polynomial and eigenpairs.
Enter your values or describe the problem in the calculator above. Review the result and the explanation before using it in homework, study or practical calculations.
Example input
e.g. eigenvalues of [[4,1],[2,3]]
How the Eigenvalues & Eigenvectors works
- Form A − λI and set its determinant to zero.
- Solve the characteristic polynomial for λ (here λ = 2 and λ = 5).
- For each λ, solve (A − λI)v = 0 to get the eigenvector.
Frequently asked questions
What is an eigenvector?
A non-zero vector that a matrix only stretches or flips: Av = λv.
What is the sum of the eigenvalues?
It equals the trace of the matrix (the sum of the diagonal entries).
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