Matrix Calculus Operations and Taylor Expansions
SIAM Review1973Vol. 15(2), pp. 352–369
Citations Over TimeTop 15% of 1973 papers
Abstract
In problems of large dimensional complexities, matrix methods are frequently the favored mathematical tools. In this paper some extensions of matrix methods to calculus operations are introduced. Consistent array structural definitions are given for derivatives of matrix-valued functions with respect to matrices, for matrix differentials, and for matrix integrals, and some operational properties arising therefrom are detailed. Novel structures are developed for Taylor expansions of a matrix-valued function, which have some attractive features both for manipulative and for computational purposes.
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