Eigenvalues and diagonalisation
Lesson 5 of 10
Finding eigenvalues
Objective. Compute eigenvalues from the characteristic equation.
The key idea
Eigenvalues satisfy det(A − λI) = 0. For a 2 × 2 matrix this reduces to λ² − (trace)λ + det = 0.
Worked example
Find the eigenvalues of A = [[2, 1], [1, 2]].
- 1Trace = 4, determinant = 3.
- 2λ² − 4λ + 3 = 0.
- 3(λ − 1)(λ − 3) = 0.
Answer: λ = 1 and λ = 3
Practice
Each question comes with a picture and a listen button. Try it first, then reveal the answer.
Common mistake. Solving det(A) − λ = 0 instead of det(A − λI) = 0.
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