A Lie product type formula in Euclidean Jordan algebras

Jiyuan Tao

Special Matrices (2016)

  • Volume: 4, Issue: 1, page 255-261
  • ISSN: 2300-7451

Abstract

top
In this paper,we state and prove an analog of Lie product formula in the setting of Euclidean Jordan algebras.

How to cite

top

Jiyuan Tao. "A Lie product type formula in Euclidean Jordan algebras." Special Matrices 4.1 (2016): 255-261. <http://eudml.org/doc/281241>.

@article{JiyuanTao2016,
abstract = {In this paper,we state and prove an analog of Lie product formula in the setting of Euclidean Jordan algebras.},
author = {Jiyuan Tao},
journal = {Special Matrices},
keywords = {Euclidean Jordan algebra; Lie product formula},
language = {eng},
number = {1},
pages = {255-261},
title = {A Lie product type formula in Euclidean Jordan algebras},
url = {http://eudml.org/doc/281241},
volume = {4},
year = {2016},
}

TY - JOUR
AU - Jiyuan Tao
TI - A Lie product type formula in Euclidean Jordan algebras
JO - Special Matrices
PY - 2016
VL - 4
IS - 1
SP - 255
EP - 261
AB - In this paper,we state and prove an analog of Lie product formula in the setting of Euclidean Jordan algebras.
LA - eng
KW - Euclidean Jordan algebra; Lie product formula
UR - http://eudml.org/doc/281241
ER -

References

top
  1. [1] R. Bhatia, Matrix Analysis, Springer Graduate Texts in Mathematics, Springer-Verlag, New York, 1997.  Zbl0863.15001
  2. [2] J. Faraut and A. Korányi, Analysis on Symmetric Cones, Clarendon Press, Oxford, 1994.  
  3. [3] M.S. Gowda, Positive and doubly stochastic maps, and majorization in Euclidean Jordan algebras, Technical Report, Department of Mathematics and Statistics, University of Maryland Baltimore County, Baltimore, MD 21250, 2016.  
  4. [4] Gerd Herzog, A proof of Lie’s product formula, The American Mathematical Monthly, Vol. 121, No.3, 254-257, 2014. [WoS] 
  5. [5] S. Lie and F. Engel, Theorie der transformationsgruppen, 3 vols. Teubner, Leipzig, 1888.  
  6. [6] B.K. Rangarajan, Polynomial convergence of infeasible-interior-point methods over symmetric cones, SIAM J. Optim., 16, 1211-1229, 2006.  Zbl1131.90043
  7. [7] J.F. Sturm, Similarity and other spectral relations for symmetric cones, Linear Alg. Appl., 312, 135-154, 2000.  Zbl0973.90093
  8. [8] J. Tao, L. Kong, Z. Luo, and N. Xiu, Somemajorization inequalities in Euclidean Jordan algebras, Linear Alg. Appl., 461, 92-122 (2014).  Zbl1352.17032
  9. [9] X. Zhan, Matrix Inequalities, Springer, 2002.  
  10. [10] F. Zhang, Quaternions and matrices of quaternions, Linear Alg. Appl. 251, 21-27 (1997).  Zbl0873.15008

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.