Timeline for Diffeomorphisms of a "matrix type"

9 events

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Apr 22, 2020 at 15:43	comment	added	Branimir Ćaćić		@New_Topologist_On_The_Block If $f : \mathbb{R}^d \to \mathbb{R}^d$ is such a map, is it obvious that the derivative $Df : \mathbb{R}^d \to \mathfrak{gl}_d(\mathbb{R})$ is pointwise invertible, so that $f$ is at least everywhere a local diffeomorphism?
Apr 22, 2020 at 9:59	history	edited	ABIM	CC BY-SA 4.0	added 50 characters in body
Apr 22, 2020 at 9:41	comment	added	ABIM		I made some edits. Basically I want to approximate all diffeomorphisms using a set of smooth modified matrix functions.
Apr 22, 2020 at 9:37	history	edited	ABIM	CC BY-SA 4.0	added 12 characters in body
Apr 22, 2020 at 9:06	history	edited	ABIM	CC BY-SA 4.0	added 18 characters in body
Apr 21, 2020 at 16:18	comment	added	Alexander Schmeding		Is it just me or why is it cleat that Y is even a subset of the diffeomorphisms? On one hand the matrix exponential is non-injective and having thought a while about this I do not see why the resulting mapping will be injective in general.
Apr 21, 2020 at 9:06	history	edited	ABIM	CC BY-SA 4.0	added 57 characters in body; edited tags
Apr 20, 2020 at 14:39	history	edited	YCor	CC BY-SA 4.0	formatting
Apr 20, 2020 at 14:05	history	asked	ABIM	CC BY-SA 4.0