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IEEE Transactions on Automatic Control
Article . 1977 . Peer-reviewed
License: IEEE Copyright
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image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
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The gradient with respect to a symmetric matrix

descriptionPublicationkeyboard_double_arrow_right Article 01 Apr 1977Publisher:Institute of Electrical and Electronics Engineers (IEEE)Journal:IEEE Transactions on Automatic Control, volume 22, pages 265-267 (issn: 0018-9286, Copyright policy )
Authors: J. Brewer;

doi: 10.1109/tac.1977.1101459

The gradient with respect to a symmetric matrix

Abstract

The well-known formulas for gradient matrices can be applied only when the elements of the matrix are independent [1],[2]. In this note, the author derives gradient formulas for two important types of element dependency: symmetry and skew symmetry. Application is made to the sensitivity analysis of optimal estimation systems.

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Keywords

Estimation and detection in stochastic control theory, Control/observation systems governed by partial differential equations

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
18
Top 10%
Top 1%
Top 10%
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