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Fungrim entry: 9e388b

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

n \in \mathbb{Z}_{\ge 0}
Definitions:
Fungrim symbol Notation Short description
RRR\mathbb{R} Real numbers
Expez{e}^{z} Exponential function
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("9e388b"),
    Formula(Implies(Element(A, Matrices(RR, n, n)), Element(Exp(A), GeneralLinearGroup(n, RR)))),
    Variables(A, n),
    Assumptions(Element(n, ZZGreaterEqual(0))))

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2021-03-15 19:12:00.328586 UTC