Finding eigenvalues
Objective. Compute eigenvalues from the characteristic equation.
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- 2. Worked example
- 3. Practice
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- 5. Continue
Learn: 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
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Start practisingCommon mistake. Solving det(A) − λ = 0 instead of det(A − λI) = 0.
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