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]]”.

Try an example:

How the Eigenvalues & Eigenvectors works

  1. Form A − λI and set its determinant to zero.
  2. Solve the characteristic polynomial for λ (here λ = 2 and λ = 5).
  3. 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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