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 />
Polinom caracteristic<br />
Defini¸tie<br />
Fie A ∈ Mn(Γ). Polinomul<br />
se nume¸ste polinom caracteristic.<br />
Teoremă<br />
Diagonalizarea matricei unei transformări<br />
Polinom caracteristic<br />
P(λ) = det(A − λIn) (9)<br />
Fie A ∈ Mn(Γ) ¸si P(λ) polinomul caracteristic. Atunci au loc:<br />
1. A ¸si A t au acela¸si polinom carateristic.<br />
2.<br />
P(λ) = (−1) n λ n + (−1) n−1 λ n−1 (a11 + a22 + · · · + ann) + · · · + an<br />
unde an = det(A).<br />
3. Date A, B ∈ Mn(Γ) ¸si C ∈ Mn(Γ) nesingulară astfel ca<br />
B = C −1 AC atunci A ¸si B au acela¸si polinom caracteristic.<br />
Transformări <strong>liniare</strong>
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