Chungbuk National University

Cheongju 28644, Republic of Korea

Office: S1-1, 404

Phone: (043) 261-2247

Email:

### Education

#### Ph. D (August, 2011), Louisiana State University .

- Thesis title: Symmetric spaces

- Supervisor: Jimmie Lawson

#### Master (August, 2007), Kyungpook National University .

- Thesis title: Converse inequalities of higher-order weighted arithmetic and geometric means of positive definite operators

- Supervisor: Yongdo Lim

#### Bachelor (August, 2005), Kyungpook National University .

### Career

#### Associate Professor

- Period: April 2017 - Current.

- Institute: Chungbuk National University, Cheongju, Korea

#### Assistant Professor

- Period: September 2013 - March 2017.

- Institute: Chungbuk National University, Cheongju, Korea

#### Research Associate

- Period: August 2011 - May 2013.

- Institute: Louisiana State University, Baton Rouge, U.S.A.

### Teaching

#### Differential Geometry ( 미분기하학 ).

#### Topics in Geometry ( 기하학 특강 ).

#### Analysis ( 해석학 ).

### Research Interest

- Matrix Analysis and Geometry
- Operator Means
- Quantum Information

### Publications

#### 30. Hosoo Lee and S. Kim, Applications of the coupled fixed point theorem to the nonlinear matrix equations, Journal of the Korean Mathematical Society, to appear. https://doi.org/10.4134/JKMS.j160793

#### 29. S. Kim, The order properties and Karcher barycenters of probability measures on the open convex cone, Taiwanese Journal of Mathematics, to appear. DOI: 10.11650/tjm/8117

#### 28. Jinmi Hwang and S. Kim, Lie-Trotter means of positive definite operators, Linear Algebra and Its Applications, 531 (2017), 268-280.

#### 27. S. Kim, The matrix geometric means under partial trace, Journal of the Chungcheong Mathematical Society, 30, No. 1 (2017), 21-29.

#### 26. Hosoo Lee and S. Kim, Muirhead's and Holland's inequalities of mixed power means for positive real numbers, Journal of Applied Mathematics and Informatics, 35, No.1-2 (2017), 33-44.

#### 25. S. Kim, Hosoo Lee, and Yongdo Lim, An order inequality characterizing invariant barycenters on symmetric cones, Journal of Mathematical Analysis and Applications, 442 (2016), 1-16.

#### 24. Hosoo Lee and S. Kim, The Hadamard product for the weighted Karcher means, Linear Algebra and Its Applications, 501 (2016), 290-303.

#### 23. Jisu Park and S. Kim, Remarks on convergence of inductive means, Journal of Applied Mathematics and Informatics, 34, No.3-4 (2016), 285-294.

#### 22. S. Kim, Gyrovector spaces on the open convex cone of positive definite matrices, Mathematics Interdisciplinary Research, Vol. 1, Issue 1 (2016), 173-185.

#### 21. S. Kim, Hosoo Lee, and Yongdo Lim, A fixed point mean approximation to the Cartan barycenter of positive definite matrices, Linear Algebra and Its Applications, 496 (2016), 420-437.

#### 20. S. Kim, Un Cig Ji, and Sangho Kum, An approach to the Log-Euclidean mean via the Karcher mean on symmetric cones, Taiwanese Journal of Mathematics, Vol. 20, Issue 1 (2016), 191-203.

#### 19. Jisu Park and S. Kim, Hilbert projective metric on a gyrogroup of qubit density matrices, Reports on Mathematical Physics, Vol. 76, Issue 3 (2015), 389-400.

#### 18. S. Kim and Hosoo Lee, Relative operator entropy related with the spectral geometric mean, Analysis and Mathematical Physics, Vol. 5, Issue 3 (2015), 233-240. DOI 10.1007/s13324-015-0099-z

#### 17. S. Kim and Denez Petz, A new proof to construct multivariable geometric means by symmetrization, Journal of Applied Math. Informatics, Vol. 33, No. 3-4 (2015), 379-386.

#### 16. S. Kim and Jimmie Lawson, Local midpoints on smooth manifolds, Differential Geometry and its Applications, 39 (2015), 129-146.

#### 15. S. Kim, Distributivity on the gyrovector spaces, Kyungpook Mathematical Journal, 55 (2015), 13-20.

#### 14. S. Kim and Hosoo Lee, The power mean and the least squares mean of probability measures on the space of positive definite matrices, Linear Algebra and Its Applications, 465 (2015), 325-346.

#### 13. S. Kim, Sungwoon Kim, and Hosoo Lee, Factorizations of invertible density matrices, Linear Algebra and Its Applications, 463 (2014), 190-204.

#### 12. Hosoo Lee and S. Kim, Multivariate coupled fixed point theorem on ordered partial metric spaces, Journal of the Korean Mathematical Society, 51, No. 6 (2014), 1189-1207.

#### 11. Hosoo Lee and S. Kim, Rado and Poponov inequalities of probability measures for positive real numbers, Journal of the Chungcheong Mathematical Society, 27, No. 2 (2014), 165-172.

#### 10. S. Kim and Jimmie Lawson, Unit balls, Lorentz boosts, and hyperbolic geometry, Results in Mathematics, 63 (2013), 1225-1242.

#### 9. Kaushik Seshadreesan, S. Kim, Jonathan Dowling, and Hwang Lee, Phase estimation at the quantum Cramer-Rao bound via parity detection, Physical Review A, 87 (2013), 043833.

#### 8. S. Kim, Operator entropy and fidelity associated with the geometric mean, Linear Algebra and Its Applications, 438 (2013), 2475-2483.

#### 7. S. Kim, Jimmie Lawson, and Yongdo Lim, The matrix geometric mean of parameterized, weighted arithmetic and harmonic means, Linear Algebra and Its Applications, 435 (2011), 2114-2131.

#### 6. S. Kim, Distances of qubit density matrices on Bloch sphere, Journal of Mathematical Physics, 52 (2011), 102303.

#### 5. S. Kim and Jimmie Lawson, Smooth Bruck loops, symmetric spaces, and nonassociative vector spaces, Demonstratio Mathematica, 44, No. 4 (2011), 755-779.

#### 4. S. Kim, Hosoo Lee, and Yongdo Lim, A sharp converse inequality of three weighted arithmetic and geometric means of positive definite operators, Mathematical Inequalities and Applications, 12, No. 3 (2009), 519-523.

#### 3. Eunkyung Ahn, S. Kim, Hosoo Lee, and Yongdo Lim, Sagae-Tanabe weighted means and reverse inequalities, Kyungpook Mathematical Journal, 47-4 (2007), 595-600.

#### 2. Eunkyung Ahn, S. Kim, and Yongdo Lim, An extended Lie-Trotter formula and its applications, Linear Algebra and Its Applications, 427 (2007), 190-196.

#### 1. S. Kim and Yongdo Lim, A converse inequality of higher order weighted arithmetic and geometric means of positive definite operators, Linear Algebra and Its Applications, 426 (2007), 490-496.

### Submitted Papers

#### 3. S. Kim, Jimmie Lawson, and Yongdo Lim, Barycentric maps for compactly supported measures, Journal of Mathematical Analysis and Applications, 2017, accepted.

#### 2. Hayoung Choi, S. Kim, and Yuanming Shi, Geometric mean of partial positive matrices with missing entries , 2017.

#### 1. S. Kim, The quasi-arithmetic means and Cartan barycenters of compactly supported measures, 2017

### Papers in Preparation

#### 6. Hana Choi, S. Kim, Hosoo Lee, and Yongdo Lim, Characterization of the $\Gamma$-commuting family of positive definite matrices, 2017.

#### 5. S. Kim, Hosoo Lee, and Yongdo Lim, A new construction of multivariate geometric means, 2017.

#### 4. S. Kim, Hosoo Lee, and Yongdo Lim, The parameterized Cartan barycenters of positive definite matrices, 2016.

#### 3. S. Kim and Hosoo Lee, Inequalities for Hadamard product of the weighted geometric means, 2016.

#### 2. Jaesung Heo, Un Cig Ji, S. Kim, and Sangho Kum, A remark on Karcher mean in monotone complete C*-algebra, 2014.

#### 1. Hosoo Lee and S. Kim, An extension of coupled fixed point theorem due to Harjani, Lopez, and Sadrangani in higher dimension, 2013.

### Some Links

#### ArXiv .

순수 수학 그 자체는 논리적인 아이디어로 구성된 시다. - Albert Einstein

만약 사람들이 수학이 단순하다고 믿지 않는다면 그것은 사람들이 인생이 얼마나 복잡한지를 깨닫지 못하기 때문이다. - John von Neumann