Title :
The gradient with respect to a symmetric matrix
Author_Institution :
University of California, Davis, CA, USA
fDate :
4/1/1977 12:00:00 AM
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.
Keywords :
Gradient methods; Linear systems, time-invariant continuous-time; Matrix functions; Sensitivity analysis; State estimation; Ash; Constraint theory; Control systems; Eigenvalues and eigenfunctions; Equations; Mechanical engineering; Polynomials; Sensitivity analysis; Symmetric matrices;
Journal_Title :
Automatic Control, IEEE Transactions on
DOI :
10.1109/TAC.1977.1101459
