Chansangiam, Pattrawut

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Chansangiam, Pattrawut
Alternative Name
Chansangiam, P.
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Email
pattrawut.ch@kmitl.ac.th

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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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    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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    Exact and least-squares solutions of a generalized Sylvester-transpose matrix equation over generalized quaternions
    (2024-01-01)
    Jaiprasert, Janthip
    ;
    Chansangiam, Pattrawut
    We have considered a generalized Sylvester-transpose matrix equation AXB + CXTD = E, where A, B,C, D, and E are given rectangular matrices over a generalized quaternion skew-field, and X is an unknown matrix. We have applied certain vectorizations and real representations to transform the matrix equation into a matrix equation over the real numbers. Thus, we have investigated a solvability condition, general exact/least-squares solutions, minimal-norm solutions, and the exact/least-squares solution closest to a given matrix. The main equation included the equation AXB = E and the Sylvester-transpose equation. Our results also covered such matrix equations over the quaternions, and quaternionic linear systems.