Do the chain rules for matrix functions hold without commutativity?
暂无分享,去创建一个
This article shows that the commutativity condition [A(t), A′(t)] = 0 is often not necessary to guarantee the chain rules for matrix functions: and where A(t) is a square matrix of differentiable functions and f is an analytic function. A further question on the chain rules is presented and discussed.
[1] Roy Mathias,et al. A Chain Rule for Matrix Functions and Applications , 1996, SIAM J. Matrix Anal. Appl..
[2] N. G. Parke,et al. Ordinary Differential Equations. , 1958 .
[3] A Remark on the Chain Rule for Exponential Matrix Functions , 2003 .
[4] Robert M Corless,et al. Some applications of the Lambert W function to physics , 2000, Canadian Journal of Physics.
[5] Charles R. Johnson,et al. Topics in Matrix Analysis , 1991 .