showing $\exp : \mathfrak{gl}(n, \mathbb{C}) \rightarrow GL(n,\mathbb{C})$ is surjective.

Asked Oct 25 '17 at 07:34

Active Oct 25 '17 at 07:41

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I want to prove $\exp : \mathfrak{gl}(n, \mathbb{C}) \longrightarrow GL(n,\mathbb{C})$ is surjective.

The textbook gives hint as "using Jordan canonical form" So my guess is expressing matrix in terms of similarity transformation, but how does it guarantee that the exponential map is surjective?

Can you give me some proof of above statement.

edited Oct 25 '17 at 07:41

José Carlos Santos

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asked Oct 25 '17 at 07:34

phy_math

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showing $\exp : \mathfrak{gl}(n, \mathbb{C}) \rightarrow GL(n,\mathbb{C})$ is surjective.

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