A simple method for solving matrix equations $ AXB = D $ and $ GXH = C $

Zhang, Huiting; Zhang, Hairui; Liu, Lina; Yuan, Yongxin

doi:10.3934/math.2021156

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2023

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Cited by 2 publications

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“…( 1). Zhang et al [7] deduced the solvability conditions for Eq. ( 1) with X * X = I p by using the matrix decompositions.…”

Section: Introductionmentioning

confidence: 99%

The Re-nonnegative definite and Re-positive definite solutions of the matrix equation AXB = C on a linear manifold

Yuan

2023

Preprint

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Let SE = { X ∈ Cn×n | ∥ XD - Z ∥F = min, D, Z ∈ Cn×q } be a linear manifold of Cn×n. We will consider the Re-nonnegative definite (Re-nnd) and Re-positive definite (Re-pd) solutions of the matrix equation AXB = C on SE , and deduce the solvability conditions for the equation as well as the explicit expressions for the general Re-nnd and Re-pd solutions when the stated conditions hold. MSC Classification: 15A24 , 15A57

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“…( 1). Zhang et al [7] deduced the solvability conditions for Eq. ( 1) with X * X = I p by using the matrix decompositions.…”

Section: Introductionmentioning

confidence: 99%

The Re-nonnegative definite and Re-positive definite solutions of the matrix equation AXB = C on a linear manifold

Yuan

2023

Preprint

Self Cite

View full text Add to dashboard Cite

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The common Re-nonnegative definite and Re-positive definite solutions to the matrix equations $ A_1XA_1^\ast = C_1 $ and $ A_2XA_2^\ast = C_2 $

Chen¹,

Liu

2021

MATH

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<abstract><p>In this paper, we consider the common Re-nonnegative definite (Re-nnd) and Re-positive definite (Re-pd) solutions to a pair of linear matrix equations $ A_1XA_1^\ast = C_1, \ A_2XA_2^\ast = C_2 $ and present some necessary and sufficient conditions for their solvability as well as the explicit expressions for the general common Re-nnd and Re-pd solutions when the consistent conditions are satisfied.</p></abstract>

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A simple method for solving matrix equations $ AXB = D $ and $ GXH = C $

Cited by 2 publications

References 29 publications

The Re-nonnegative definite and Re-positive definite solutions of the matrix equation AXB = C on a linear manifold

The Re-nonnegative definite and Re-positive definite solutions of the matrix equation AXB = C on a linear manifold

The common Re-nonnegative definite and Re-positive definite solutions to the matrix equations $ A_1XA_1^\ast = C_1 $ and $ A_2XA_2^\ast = C_2 $

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