An extended Lie-Trotter formula and its applications

Linear Algebra and Its Applications

Volumn 427, Issue 2-3, 2007, Pages 190-196

  Ahn, Eunkyung ^a   Kim, Sejung ^a   Lim, Yongdo ^a  

^a Kyungpook National University   (South Korea)

Author keywords

Geometric mean; Lie Trotter formula; Log Euclidean mean; Positive definite operator; Sagae Tanabe mean; Spectral geometric mean

Indexed keywords

COMPUTATIONAL GEOMETRY; LINEAR ALGEBRA; MEAN FIELD THEORY;

HERMITIAN OPERATORS; HIAI-PETZ; LIE-TROTTER FORMULA; SAGAE-TANABE MEAN; SPECTRAL GEOMETRIC MEAN;

MATHEMATICAL OPERATORS;

EID: 34648835392     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.laa.2007.07.011     Document Type: Article

References (16)

1. Ando T. Hadamard products and Golden-Thompson type inequalities. Linear Algebra Appl. 241/243 (1996) 105-112
2. Arsigny V., Fillard P., Pennec X., and Ayache N. Geometric means in a noval vector space structure on symmetric positive-definite matrices. SIAM.J. Matrix Anal. Appl. 29 (2006) 328-347
3. Bebiano N., Lemos R., and da Providência J. Inequalities for quantum relative entropy. Linear Algebra Appl. 401 (2005) 159-172
4. Bhatia R. Matrix Analysis. Graduate Texts in Mathematics (1996), Springer-Verlag
5. Corach G., Porta H., and Recht L. Convexity of the geodesic distance on spaces of positive operators. Illinois J. Math. 38 (1994) 87-94
6. Faybusovich L. A Jordan-algebraic approach to potential-reduction algorithms. Math. Z. 239 (2002) 117-129
7. Fiedler M., and Pták V. A new positive definite geometric mean of two positive definite matrices. Linear Algebra Appl. 251 (1997) 1-20
8. Fujii M., and Nakamoto R. A geometric mean in the Furuta inequality. Sci. Math. Jpn. 55 (2002) 615-621
9. Furuta T. Convergence of logarithmic trace inequalities via generalized Lie-Trotter formulae. Linear Algebra Appl. 396 (2005) 353-372
10. Hiai F., and Petz D. The Golden-Thompson trace inequality is complemented. Linear Algebra Appl. 181 (1993) 153-185
11. Howe R. Very basic Lie theory. Amer. Math. Monthly 90 (1983) 600-624
12. Moakher M. A differential geometric approach to the geometric mean of symmetric positive-definite matrices. SIAM J. Matrix Anal. Appl. 26 (2005) 735-747
13. Moakher M. On the averaging of symmetric positive-definite tensors. J. Elasticity 82 (2006) 273-296
14. Nussbaum R.D. Hilbert's projective metric and iterated nonlinear maps. Memoirs of Amer. Math. Soc. 391 (1988)
15. Sagae M., and Tanabe K. Upper and lower bounds for the arithmetic-geometric-harmonic means of positive definite matrices. Linear and Multilinear Algebras 37 (1994) 279-282
16. Thompson A.C. On certain contraction mappings in a partially ordered vector space. Proc. Amer. Math. Soc. 14 (1963) 438-443