Chansangiam, Pattrawut

Preferred name

Alternative Name

Chansangiam, P.

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School of Science

pattrawut.ch@kmitl.ac.th

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Weighted Lim’s geometric mean of positive invertible operators on a Hilbert space
(2020-03-01)
Ploymukda, Arnon
;
Chansangiam, Pattrawut
We generalize the weighted Lim’s geometric mean of positive definite matrices to positive invertible operators on a Hilbert space. This mean is defined via a certain bijection map and parametrized over Hermitian unitary operators. We derive an explicit formula of the weighted Lim’s geometric mean in terms of weighted metric/spectral geometric means. This kind of operator mean turns out to be a symmetric Lim-Pálfia weighted mean and satisfies the idempotency, the permutation invariance, the joint homogeneity, the self-duality, and the unitary invariance. Moreover, we obtain relations between weighted Lim geometric means and Tracy-Singh products via operator identities.
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Inequalities for Kronecker products and Hadamard products of positive definite matrices
(2009-01-01)
Chansangiam, Pattrawut
;
Hemchote, Patcharin
;
Pantaragphong, Praiboon
The purpose of this paper is to develop inequalities for Kronecker products and Hadamard products of positive definite matrices. A number of inequalities involving powers, Kronecker powers, and Hadamard powers of linear combination of matrices are presented. In particular, Hölder inequalities and arithmetic mean-geometric mean inequalities for Kronecker products and Hadamard products are obtained as special cases.
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THE GEOMETRY ON THE SLOPE OF A MOUNTAIN
(2020-01-01)
Chansri, P.
;
Chansangiam, P.
;
Sabau, Sorin V.
The geometry on a slope of a mountain is the geometry of a Finsler metric, called here the slope metric. We study the existence of globally defined slope metrics on surfaces of revolution as well as the geodesic’s behavior. A comparison between Finslerian and Riemannian areas of a bounded region is also studied.
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Convexity and monotonicity of certain maps involving hadamard products and bochner integrals for continuous fields of operators
(2019-10-30)
Chansangiam, Pattrawut
We investigate the convexity and the monotonicity of certain maps involving Hadamard products and Bochner integrals for continuous fields of Hilbert space operators. Their special cases and consequences are then discussed. In particular, we obtain certain arithmetic mean-harmonic mean, Jensen, and Fiedler type inequalities.
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On the existence of convex functions on Finsler manifolds
(2019-01-01)
Sabau, Sorin Vasile
;
Chansangiam, Pattrawut
We show that a non-compact (forward) complete Finsler manifold whose Holmes-Thompson volume is finite admits no non-trivial convex functions. We apply this result to some Finsler manifolds whose Busemann function is convex.
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Least-squares solutions of generalized linear systems and the matrix equation AXB = C under the general semi-tensor products
(2026-01-01)
Jaiprasert, Janthip
;
Phoonphiphat, Thanaphon
;
Chansangiam, Pattrawut
;
Zhang, Yang
We investigate least-squares (LS) solutions of Sylvester-type matrix equations formulated via the general semi-tensor product (GSTP) of matrices. In particular, we consider generalized linear systems of the form A (Formula presented) x = B, where A and B are given rectangular matrices and x is an unknown column vector, with k denoting the GSTP that extends both the conventional matrix product and the semi-tensor product. By analyzing the derivative of the LS error associated with the equation, we show that LS solutions can be obtained by solving an equivalent linear system under the usual matrix product. Using matrix partitioning techniques, these results are further extended to several Sylvester-type equations, including A (Formula presented) X = B, X (Formula presented) A = B. and A (Formula presented) X x B = C, where X is an unknown matrix of compatible size. This framework unifies the classical and semi-tensor product cases under a generalized algebraic setting. Furthermore, we develop a gradient-descent iterative algorithm to compute approximate LS solutions efficiently. Numerical experiments confirm the convergence, capability, and effectiveness of the proposed method.
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Riccati equation and metric geometric means of positive semidefinite matrices involving semi-tensor products
(2023-01-01)
Chansangiam, Pattrawut
;
Ploymukda, Arnon
We investigate the Riccati matrix equation XA<sup>−1</sup>X = B in which the conventional matrix products are generalized to the semi-tensor products ⋉. When A and B are positive definite matrices satisfying the factor-dimension condition, this equation has a unique positive definite solution, which is defined to be the metric geometric mean of A and B. We show that this geometric mean is the maximum solution of the Riccati inequality. We then extend the notion of the metric geometric mean to positive semidefinite matrices by a continuity argument and investigate its algebraic properties, order properties and analytic properties. Moreover, we establish some equations and inequalities of metric geometric means for matrices involving cancellability, positive linear map and concavity. Our results generalize the conventional metric geometric means of matrices.
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Integral inequalities of chebyshev type for continuous fields of Hermitian operators involving Tracy-Singh products and weighted pythagorean means
(2019-10-01)
Ploymukda, Arnon
;
Chansangiam, Pattrawut
In this paper, we establish several integral inequalities of Chebyshev type for bounded continuous fields of Hermitian operators concerning Tracy-Singh products and weighted Pythagorean means. The weighted Pythagorean means considered here are parametrization versions of three symmetric means: the arithmetic mean, the geometric mean, and the harmonic mean. Every continuous field considered here is parametrized by a locally compact Hausdorff space equipped with a finite Radon measure. Tracy-Singh product versions of the Chebyshev-Grüss inequality via oscillations are also obtained. Such integral inequalities reduce to discrete inequalities when the space is a finite space equipped with the counting measure. Moreover, our results include Chebyshev-type inequalities for tensor product of operators and Tracy-Singh/Kronecker products of matrices.
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Solving the Sylvester-Transpose Matrix Equation under the Semi-Tensor Product
(2022-06-01)
Jaiprasert, Janthip
;
Chansangiam, Pattrawut
This paper investigates the Sylvester-transpose matrix equation A ⋉ X + X<sup>T</sup> ⋉ B = C, where all mentioned matrices are over an arbitrary field. Here, ⋉ is the semi-tensor product, which is a generalization of the usual matrix product defined for matrices of arbitrary dimensions. For matrices of compatible dimensions, we investigate criteria for the equation to have a solution, a unique solution, or infinitely many solutions. These conditions rely on ranks and linear dependence. Moreover, we find suitable matrix partitions so that the matrix equation can be transformed into a linear system involving the usual matrix product. Our work includes the studies of the equation A ⋉ X = C, the equation X ⋉ B = C, and the classical Sylvester-transpose matrix equation.
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Jensen’s type inequalities involving tracy-singh products, khatri-rao products, tracy-singh sums and khatri-rao sums
(2020-01-01)
Ploymukda, Arnon
;
Chansangiam, Pattrawut
In this paper, we establish a number of Jensen’s type inequalities for Hilbert space operators involving convex/concave functions, unital positive linear maps, and certain operator products and sums. The products and sums considered here include the Tracy-Singh product, the Khatri-Rao products, the Tracy-Singh sum, and the Khatri-Rao sum. Moreover, we generalize Jensen’s type inequalities in term of functional calculus of two-variable functions. In particular, we obtain Kantorovich-type operator inequalities involving the products and sums.

Chansangiam, Pattrawut

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