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Characteristic and minimal polynomials

General · Mathematics

Study notes

Q: Find characteristic and minimal polynomials of [[2,1],[0,2]]. χ(λ) = det[[2-λ,1],[0,2-λ]] = (2-λ)² = λ²-4λ+4. Minimal: try (A-2I): [[0,1],[0,0]] ≠ 0. (A-2I)² = 0 ✓: m(λ) = (λ-2)². Here m = χ (defective - not diagonalizable!)!

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