Intrinsic representation of tangent vectors and vector transports on matrix manifolds

2016 ◽  
Vol 136 (2) ◽  
pp. 523-543 ◽  
Author(s):  
Wen Huang ◽  
P.-A. Absil ◽  
K. A. Gallivan
Keyword(s):  
Matrix Manifolds ◽  
Tangent Vectors

scholarly journals Expanding endomorphisms of the circle revisited

1985 ◽  
Vol 5 (2) ◽  
pp. 285-289 ◽  
Author(s):  
Michael Shub ◽  
Dennis Sullivan
Keyword(s):  
Expanding Maps ◽  
Tangent Vectors

AbstractTwo Cr, r ≥ 2, expanding maps of the circle which are absolutely continuously conjugate are Cr conjugate. Here ƒ and g: S1 → S1 are expanding if they stretch tangent vectors in some metric, and a conjugacy is an isomorphism h: S1 → S1 such that fh = hg.

Matrix manifolds in MDA

2021 ◽  
pp. 45-88
Author(s):  
Nickolay Trendafilov ◽  
Michele Gallo
Keyword(s):  
Matrix Manifolds

scholarly journals The Structured Condition Number of a Differentiable Map between Matrix Manifolds, with Applications

2019 ◽  
Vol 40 (2) ◽  
pp. 774-799
Author(s):  
Bahar Arslan ◽  
Vanni Noferini ◽  
Françoise Tisseur
Keyword(s):  
Condition Number ◽  
Matrix Manifolds

scholarly journals Tangent vectors to sets in the theory of geodesics

1987 ◽  
Vol 106 ◽  
pp. 29-47 ◽  
Author(s):  
Dumitru Motreanu
Keyword(s):  
Closed Subset ◽  
Tangent Vector ◽  
General Concept ◽  
Recent Book ◽  
Closed Sets ◽  
Banach Manifolds ◽  
Flow Invariance ◽  
Tangent Vectors

In the setting of Banach manifolds the notion of tangent vector to an arbitrary closed subset has been introduced in [11] by the author and N. H. Pavel, and it has been used in flow-invariance and optimization ([11], [12], [13]). For detailed informations on tangent vectors to closed sets (including historical comments) we refer to the recent book of N. H. Pavel [17].The aim of this paper is to apply this general concept of tangency in the study of geodesies. We are concerned with geodesies which have either the endpoints in given closed subsets or the same angle for a fixed closed subset. This approach allows one to extend important results due to K. Grove [4] and T. Kurogi ([6], [7]).

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