Let $GL(n, \mathbb{C})$ be the complex general linear (Lie) group consisting of all invertible complex $n\times n$ matrices, and $gl(n,\mathbb{C})\cong C^{n^2}$ be its Lie algebra. The exponential map of matrix groups are defined by the usual infinite series. I think since all entries are infinite series this map is holomorphic between these two complex manifold. Is this correct?
2026-03-25 06:04:55.1774418695
Is the exponential map of GL(n,C) holomorphic?
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