Operator means
(with Dumitru Raluca and Jose Franco) The alternative Heinz means of matrices, Linear and Multilinear Algebra, DOI: doi.org/10.1080/03081087.2025.2564162
(with Dumitru Raluca, Jose Franco and Malgorzata Czerwinska) A theory of alternative means of positive operators, Journal of Mathematical Analysis and Applications (2025), DOI: doi.org/10.1016/j.jmaa.2025.130129
(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.