Transformari liniare
Transformari liniare
Transformari liniare
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No¸tiunea de transformare liniară<br />
Transformări <strong>liniare</strong> între spa¸tii finit dimensionale<br />
Valori ¸si vectori proprii<br />
Demonstra¸tie<br />
Diagonalizarea matricei unei transformări<br />
Polinom caracteristic<br />
P(λ) = (a11−λ)(a22−λ) · · · (ann−λ)+polinom de grad ≤ n−2 =<br />
(−1) n λ n + (−1) n−1 (a11 + a22 + · · · + ann)λ n−1 + · · · + an.<br />
Dacă λ = 0 deducem an = det(A).<br />
Consecin¸te.<br />
1 λ1 + λ2 + · · · + λn = Tr(A)<br />
2. λ1 · λ2 · · · λn = det(A).<br />
Transformări <strong>liniare</strong>