Notes on the history of Liouville’s theorem
نویسنده
چکیده
2 Autonomous differential equations Lemma 1. If A ∈ B(R), then det(I + A+ o( )) = 1 + trA+ o( ) as → 0. Proof. Let λ1, . . . , λn be the eigenvalues of A, repeated according to algebraic multiplicity. For > 0, the eigenvalues of I + A + o( ) repeated according to algebraic multiplicity are 1 + λ1 + o( ), . . . , 1 + λn + o( ), as → 0. The determinant of a linear map R → R is the product of its eigenvalues according to algebraic multiplicity, so
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