Fungrim entry: 9e388b

A \in \operatorname{M}_{n \times n}\!\left(\mathbb{R}\right) \;\implies\; {e}^{A} \in \operatorname{GL}_{n}\!\left(\mathbb{R}\right)

Assumptions:

n \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
`RR`	$\mathbb{R}$	Real numbers
`Exp`	${e}^{z}$	Exponential function
`ZZGreaterEqual`	$\mathbb{Z}_{\ge n}$	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))))

Topics using this entry

Exponential function

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