On Some Matrix Trace Inequalities

Ulukök, Zübeyde; Türkmen, Ramazan

doi:10.1155/2010/201486

Cited by 21 publications

(18 citation statements)

References 8 publications

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“…If A and B are positive semi-definite matrices, then 0 ≤ Tr(A B) ≤ Tr(A)Tr(B) [10]. Defining A ≡ b true 1 (b true 1 ) TF and B ≡F shows that the inequality in Eq.…”

Section: Optimality Conditionmentioning

confidence: 99%

Generalized Attitude Determination with One Dominant Vector Observation

Cheng

2019

Journal of Guidance, Control, and Dynamics

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This paper derives an algorithm to determine the approximate attitude of a vehicle from both vector and arc-length observations, which are the most general types of attitude observations. It is assumed that one of the vector observations is more accurate than the other vector and arc-length observations. The solution is found by solving a quartic polynomial equation. Then the quaternion can be determined from the polynomial solution. The attitude errorcovariance is also derived using both an attitude perturbation approach and a constrained least squares approach. Both are shown to yield identical results. An optimality condition is also derived that compares the derived suboptimal error-covariance with the optimal one. Several special cases, such as a set of one direction observation and an arc-length observation, are shown. Simulation results using a Monte Carlo analysis are shown to verify the derived algorithm.

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“…If A and B are positive semi-definite matrices, then 0 ≤ Tr(A B) ≤ Tr(A)Tr(B) [10]. Defining A ≡ b true 1 (b true 1 ) TF and B ≡F shows that the inequality in Eq.…”

Section: Optimality Conditionmentioning

confidence: 99%

Generalized Attitude Determination with One Dominant Vector Observation

Cheng

2019

Journal of Guidance, Control, and Dynamics

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“…For some classical trace inequalities see [4], [6], [30] and [38], which are continuations of the work of Bellman [2]. For related works the reader can refer to [1], [3], [4], [14], [22], [27], [28], [31] and [35].…”

Section: Trace Of Operatorsmentioning

confidence: 99%

Some inequalities for trace class operators via a Kato’s result

Dragomir¹

2017

Asian-European J. Math.

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“…For some classical trace inequalities see [20][21][22][23][24], which are continuations of the work of Bellman [25]. For related works the reader can refer to [20,24,[26][27][28][29][30][31][32].…”

Section: Trace Of Operatorsmentioning

confidence: 99%