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In these notes, we consider the problem of finding the logarithm or the square root of a real matrix.
Théorie élémentaire des fonctions analytiques d’une ou plusieurs variables complexes
Henri Cartan · 1961
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Cours d’Algèbre
Roger Godement · 1963
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On the existence and uniqueness of the real logarithm of a matrix
Walter J. Culver · 1966
Earlier work this paper cites.
Linear Algebra
Hoffman Kenneth and Kunze Ray · 1971
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The range of A − 1 A ∗ A^{-1}A^{*} in 𝐆𝐋 ( n , 𝐂 ) \mathbf{GL}(n,\mathbf{C})
C. R. DePrima and C. R. Johnson · 1974
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Differential Equations, Dynamical Systems and Linear Algebra
Morris W. Hirsh and Stephen Smale · 1974
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The Theory of Matrices, Vol. I
F.R. Gantmacher · 1977
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Algèbre, Chapitres 4-7
Nicolas Bourbaki · 1981
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Computing real square roots of a real matrix
Nicholas J. Higham · 1987
Earlier work this paper cites.
Linear Algebra and its Applications
Gilbert Strang · 1988
Cited alongside, same era.
Elements of Mathematics. Lie Groups and Lie Algebras, Chapters 1–3
Nicolas Bourbaki · 1989
Cited alongside, same era.
Condition estimates for matrix functions
Charles S. Kenney and Alan J. Laub · 1989
Cited alongside, same era.
Matrix Analysis
Roger A. Horn and Charles R. Johnson · 1990
Cited alongside, same era.
Topics in Matrix Analysis
Roger A. Horn and Charles R. Johnson · 1994
Cited alongside, same era.
Introduction à la Théorie des Groupes de Lie Classiques
R. Mneimné and F. Testard · 1997
Cited alongside, same era.
Abstract Algebra
David S. Dummit and Richard M. Foote · 1999
Polyrigid and polyaffine transformations: a novel geometrical tool to deal with non-rigid deformations–application to the registration of histological slices
Vincent Arsigny, Xavier Pennec, and Nicholas Ayache · 2005
Later among the works it cites.
Algorithms for the matrix pth root
Dario A. Bini, Nicholas J. Higham, and Beatrice Meini · 2005
Later among the works it cites.
Processing Data in Lie Groups: An Algebraic Approach. Application to Non-Linear Registration and Diffusion Tensor MRI
Vincent Arsigny · 2006
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A fast and log-euclidean polyaffine framework for locally affine registration
Vincent Arsigny, Olivier Commowick, Xavier Pennec, and Nicholas Ayache · 2006
Later among the works it cites.
Log-euclidean metrics for fast and simple calculus on diffusion tensors
Vincent Arsigny, Pierre Fillard, Xavier Pennec, and Nicholas Ayache · 2006
Later among the works it cites.
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Cited alongside, same era.
Complex Analysis
Serge Lang · 1999
Cited alongside, same era.
Approximating the logarithm of a matrix to specified accuracy
Sheung H. Cheng, Nicholas J. Higham, Charles Kenney, and Alan J. Laub · 2001
Cited alongside, same era.
Geometric means in a novel vector space structure on symmetric positive-definite matrices
Vincent Arsigny, Pierre Fillard, Xavier Pennec, and Nicholas Ayache · 2007
Later among the works it cites.
Functions of Matrices. Theory and Computation
Nicholas J. Higham · 2008
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Matrices, Theory and Applications
Denis Serre · 2010
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