Inequalities of generalized matrix functions via tensor products

Paksoy, Vehbi Emrah; Türkmen, Ramazan; Zhang, Fuzhen

doi:10.13001/1081-3810.1622

Cited by 15 publications

(13 citation statements)

References 4 publications

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“…This line of thought is wellknown in matrix analysis, see e.g. [Bhatia, 2007, p. 114] and also [Paksoy et al, 2014].…”

Section: Notation and Backgroundmentioning

confidence: 77%

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Hlawka–Popoviciu inequalities on positive definite tensors

Berndt¹,

Sra²

2015

Linear Algebra and its Applications

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We prove inequalities on symmetric tensor sums of positive definite operators. In particular, we prove multivariable operator inequalities inspired by generalizations to the wellknown Hlawka and Popoviciu inequalities. As corollaries, we obtain generalized Hlawka and Popoviciu inequalities for determinants, permanents, and generalized matrix functions. The new operator inequalities and their corollaries contain a few recently published inequalities on positive definite matrices as special cases.

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“…This line of thought is wellknown in matrix analysis, see e.g. [Bhatia, 2007, p. 114] and also [Paksoy et al, 2014].…”

Section: Notation and Backgroundmentioning

confidence: 77%

“…Corollary 4.4 combined with the superadditivity inequality Prop. 1.1(iv) for the appropriate pairs of indices implies the following result ofPaksoy et al [2014].…”

mentioning

confidence: 78%

Hlawka–Popoviciu inequalities on positive definite tensors

Berndt¹,

Sra²

2015

Linear Algebra and its Applications

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“…Notice that, for two positive semidefinite matrices A 1 and A 2 , there holds det (A 1 + A 2 ) ≥ det (A 1 ) + det (A 2 ). 35,36 Thus, we have…”

Section: Proof Of Lemmamentioning

confidence: 99%

Data‐driven–based attitude control of combined spacecraft with noncooperative target

Jiang

Zhou

et al. 2019

Intl J Robust & Nonlinear

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Summary In this paper, the attitude control of combined spacecraft with noncooperative target is studied. For the linearized system of the attitude control system, which possesses uncertainties on both its control and system matrices caused by the noncooperative target, this paper proposes an approximated iteration method to obtain the optimal controller such that the closed‐loop system possesses a prescribed convergence rate. An explicit stabilizing gain is established to initiate the iteration method. Based on the proposed iteration method and the initial stabilizing gain, a data‐driven algorithm is proposed to obtain the optimal controller for the attitude control system without using the system parameter information. A simulation is given to verify the effectiveness of the proposed method.

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“…Firstly, we introduce the definition of partial matrix functions corresponding to partial traces and partial determinants, and then we provide a unified extension of a recent result of Lin [10], Chang-Paksoy-Zhang [4] and Lin-Sra [12]. Secondly, we give a new generalization of a result of Paksoy-Turkmen-Zhang [15]. Finally, we conclude with an interesting conjecture involving partial determinants.…”

mentioning

confidence: 90%

Partial determinant inequalities for positive semidefinite block matrices

Li¹,

Lin²,

Feng³

2021

Journal of Mathematical Inequalities

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We present some inequalities related to partial determinants for positive semidefinite block matrices. Firstly, we introduce the definition of partial matrix functions corresponding to partial traces and partial determinants, and then we provide a unified extension of a recent result of Lin [10], Chang-Paksoy-Zhang [4] and Lin-Sra [12]. Secondly, we give a new generalization of a result of Paksoy-Turkmen-Zhang [15]. Finally, we conclude with an interesting conjecture involving partial determinants.

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Inequalities of generalized matrix functions via tensor products

Abstract: By an embedding approach and through tensor products, some inequalities for generalized matrix functions (of positive semidefinite matrices) associated with any subgroup of the permutation group and any irreducible character of the subgroup are obtainned.

Cited by 15 publications

References 4 publications

Hlawka–Popoviciu inequalities on positive definite tensors

Hlawka–Popoviciu inequalities on positive definite tensors

Data‐driven–based attitude control of combined spacecraft with noncooperative target

Partial determinant inequalities for positive semidefinite block matrices

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