Operator means
(with Huajun Huang and Vatsalkumar N. Mer) Operator mean and mean iterations of positive constant upper triangular matrices, Electronic Journal of Linear Algebra, 42 (2026), 294-313.
(with Dumitru Raluca, Jose Franco and Malgorzata Czerwinska) A theory of alternative means of positive operators, Journal of Mathematical Analysis and Applications 556 (2026), 130129.
(with Dumitru Raluca and Jose Franco) The alternative Heinz means of matrices, Linear and Multilinear Algebra, 73 (2025), no. 17, 3809-3824.
(with Jose Franco and Luyining Gan) Near-geometric mean of positive definite operators, Postivity (2025), 29:54.
(with Dumitru Raluca and Jose Franco) Quasi-Wasserstein means of matrices, Results in Mathematics (2025), 80:170
(with Dumitru Raluca and Jose Franco) In-betweenness and Heinz mean inequalities, Banach Journal of Mathematical Analysis (2025) 19:38.
(with Jinmi Hwang) Near-order relation of power means, Postivity (2025), 29:3, DOI: doi.org/10.1007/s11117-024-01099-4
(with Vatsalkumar N. Mer) New multivariable mean from nonlinear matrix equation associated to the harmonic mean, Acta Scientiarum Mathematicarum, 90 (2024), Issue 3-4, 605-622.
(with Vatsalkumar N. Mer) The Wasserstein mean of unipotent matrices, Linear and Multilinear Algebra, 72 (2024), no. 16, 2732-2748.
(with Luyining Gan) Revisit on spectral geometric mean, Linear and Multilinear Algebra, 72 (2024), no. 6, 944-955.
(with Hayoung Choi and Yongdo Lim) A binomial expansion formula for weighted geometric means of unipotent matrices, Linear and Multilinear Algebra, 72 (2024), no. 4, 615-630.
(with Luyining Gan) Weak log-majorization between the geometric and Wasserstein means, Journal of Mathematical Analysis and Applications, 530, No. 2 (2024), 127711.
(with Hayoung Choi and Yongdo Lim) Linearity of Cartan and Wasserstein means, Linear Algebra and Its Applications, 681 (2024), 66-88.
(with Miran Jeong) Weak log-majorization and inequalities of power means, Electronic Journal of Linear Algebra, 39 (2023), 607-620.
(with Miran Jeong and Jinmi Hwang) Right mean for the α−z Bures-Wasserstein quantum divergence, Acta Mathematica Scientia, 43, No. 5 (2023), 2320-2332.
Parameterized Wasserstein means, Journal of Mathematical Analysis and Applications, 525, No. 1 (2023), 127272.
(with Byoung Jin Choi) Logarithmic mean of positive invertible operators, Banach Journal of Mathematical Analysis, Vol. 17, Issue 2 (2023), 20.
Operator power means in the view of fixed points, Complex Analysis and Operator Theory, Vol. 16, No. 8 (2022), 118.
Mixture and interpolation of the parameterized ordered means, Journal of Inequalities and Applications, 2022 (2022), 119.
(with Jinmi Hwang) Two-variable Wasserstein means of positive definite operators, Mediterranean Journal of Mathematics, 19, No. 3 (2022), 110.
(with Hosoo Lee) Wasserstein barycenters of compactly supported measures, Analysis and Mathematical Physics, Vol. 11, Issue 4 (2021).
Operator inequalities and gyrolines of the weighted geometric means, Mathematical Inequalities and Applications, 24, No. 2 (2021), 491-514.
(with Hayoung Choi and Yuanming Shi) Geometric mean of partial positive definite matrices with missing entries, Linear and Multilinear Algebra, 68, No. 12 (2020), 2408-2433.
(with Jinmi Hwang) Tensor product and Hadamard product for the Wasserstein means, Linear Algebra and Its Applications, 603 (2020), 496-507.
(with Hana Choi, Hayoung Choi and Hosoo Lee) Extension of block matrix representation of the geometric mean, Journal of the Korean Mathematical Society, 57, No. 3 (2020), 641-653.
(with Hosoo Lee) Inequalities of the Wasserstein mean with other matrix means, Annals of Functional Analysis, 11, No. 1 (2020), 194-207.
(with Hosoo Lee and Yongdo Lim) Geometric mean block matrices, Linear Algebra and Its Applications, 575 (2019), 299-313.
(with Jinmi Hwang) Bounds for the Wasserstein mean with applications to the Lie-Trotter mean, Journal of Mathematical Analysis and Applications, 475, No. 2 (2019), 1744-1753.
(with Hosoo Lee and Yongdo Lim) Repetition invariant geometric means, Linear Algebra and Its Applications, 544 (2018), 443-459.
The quasi-arithmetic means and Cartan barycenters of compactly supported measures, Forum Mathematicum, 30, No. 3 (2018), 753-765.
(with Jimmie Lawson and Yongdo Lim) Barycentric maps for compactly supported measures, Journal of Mathematical Analysis and Applications, 458 (2016), 1009-1026.
The order properties and Karcher barycenters of probability measures on the open convex cone, Taiwanese Journal of Mathematics, 22 (2018), 79-94.
(with Jinmi Hwang) Lie-Trotter means of positive definite operators, Linear Algebra and Its Applications, 531 (2017), 268-280.
(with Hosoo Lee and Yongdo Lim) An order inequality characterizing invariant barycenters on symmetric cones, Journal of Mathematical Analysis and Applications, 442 (2016), 1-16.
(with Hosoo Lee) The Hadamard product for the weighted Karcher means, Linear Algebra and Its Applications, 501 (2016), 290-303.
(with 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.
(with 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.
(with 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.
(with 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.
(with 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.
(with Eunkyung Ahn and Yongdo Lim) An extended Lie-Trotter formula and its applications, Linear Algebra and Its Applications, 427 (2007), 190-196.
(with 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.
Matrix Analysis and geometry
(with Jinmi Hwang and Vatsalkumar N. Mer) Non-homogeneous Riemannian gradient equations for sum of squares of Bures-Wasserstein metric, Journal of Computational and Applied Mathematics, 438 (2024), 115555.
Ordered gyrovector space, Symmetry, 12, No. 6 (2020), 1041.
(with Hayoung Choi, Hosoo Lee and Yongdo Lim) Matrix extremal problems and shift invariant means, Linear Algebra and Its Applications, 587 (2020), 166-194.
(with Hosoo Lee) Applications of the coupled fixed point theorem to the nonlinear matrix equations, Journal of the Korean Mathematical Society, 55, No. 1 (2018), 73-82.
(with Jimmie Lawson) Local midpoints on smooth manifolds, Differential Geometry and its Applications, 39 (2015), 129-146.
(with Sungwoon Kim and Hosoo Lee) Factorizations of invertible density matrices, Linear Algebra and Its Applications, 463 (2014), 190-204.
(with Hosoo Lee) Multivariate coupled fixed point theorem on ordered partial metric spaces, Journal of the Korean Mathematical Society, 51, No. 6 (2014), 1189-1207.
(with Jimmie Lawson) Unit balls, Lorentz boosts, and hyperbolic geometry, Results in Mathematics, 63 (2013), 1225-1242.
(with Jimmie Lawson) Smooth Bruck loops, symmetric spaces, and nonassociative vector spaces, Demonstratio Mathematica, 44, No. 4 (2011), 755-779.
Quantum information and quantum computation
(with Miran Jeong and Tin-Yau Tam) New weighted spectral geometric mean and quantum divergence, Linear Algebra and Its Applications, 726 (2025), 164-179.
(with Miran Jeon) Barycenter of the arithmetic-harmonic quantum divergence, Electronic Journal of Linear Algebra, 41 (2025), 236-247.
(with Luyining Gan and Miran Jeong) Quantum divergence and barycenter associated with the spectral geometric mean, Linear Algebra and Its Applications, 721 (2025), 449-464.
Fidelity and metrics on Lorentz boosts, Journal of Lie Theory, 30, No. 2 (2020), 445-459.
(with Jisu Park) Hilbert projective metric on a gyrogroup of qubit density matrices, Reports on Mathematical Physics, Vol. 76, Issue 3 (2015), 389-400.
(with Hosoo Lee) Relative operator entropy related with the spectral geometric mean, Analysis and Mathematical Physics, Vol. 5, Issue 3 (2015), 233-240.
(with Kaushik Seshadreesan, Jonathan Dowling, and Hwang Lee) Phase estimation at the quantum Cramer-Rao bound via parity detection, Physical Review A, 87 (2013), 043833.
Operator entropy and fidelity associated with the geometric mean, Linear Algebra and Its Applications, 438 (2013), 2475-2483.
Distances of qubit density matrices on Bloch sphere, Journal of Mathematical Physics, 52 (2011), 102303.