Fungrim home page

Fungrim entry: 2ea614

AMn×n ⁣(C)        eAGLn ⁣(C)A \in \operatorname{M}_{n \times n}\!\left(\mathbb{C}\right) \;\implies\; {e}^{A} \in \operatorname{GL}_{n}\!\left(\mathbb{C}\right)
Assumptions:nZ0n \in \mathbb{Z}_{\ge 0}
A \in \operatorname{M}_{n \times n}\!\left(\mathbb{C}\right) \;\implies\; {e}^{A} \in \operatorname{GL}_{n}\!\left(\mathbb{C}\right)

n \in \mathbb{Z}_{\ge 0}
Fungrim symbol Notation Short description
CCC\mathbb{C} Complex numbers
Expez{e}^{z} Exponential function
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
    Formula(Implies(Element(A, Matrices(CC, n, n)), Element(Exp(A), GeneralLinearGroup(n, CC)))),
    Variables(A, n),
    Assumptions(Element(n, ZZGreaterEqual(0))))

Topics using this entry

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC